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Simplifying 1000x + 50x + 90x + 53x + -12x * 5x = 9x + 62x + 68x + 32 + 62 Reorder the terms for easier multiplication: 1000x + 50x + 90x + 53x + -12 * 5x * x = 9x + 62x + 68x + 32 + 62 Multiply -12 * 5 1000x + 50x + 90x + 53x + -60x * x = 9x + 62x + 68x + 32 + 62 Multiply x * x 1000x + 50x + 90x + 53x + -60x2 = 9x + 62x + 68x + 32 + 62 Combine like terms: 1000x + 50x = 1050x 1050x + 90x + 53x + -60x2 = 9x + 62x + 68x + 32 + 62 Combine like terms: 1050x + 90x = 1140x 1140x + 53x + -60x2 = 9x + 62x + 68x + 32 + 62 Combine like terms: 1140x + 53x = 1193x 1193x + -60x2 = 9x + 62x + 68x + 32 + 62 Reorder the terms: 1193x + -60x2 = 32 + 62 + 9x + 62x + 68x Combine like terms: 32 + 62 = 94 1193x + -60x2 = 94 + 9x + 62x + 68x Combine like terms: 9x + 62x = 71x 1193x + -60x2 = 94 + 71x + 68x Combine like terms: 71x + 68x = 139x 1193x + -60x2 = 94 + 139x Solving 1193x + -60x2 = 94 + 139x Solving for variable 'x'. Reorder the terms: -94 + 1193x + -139x + -60x2 = 94 + 139x + -94 + -139x Combine like terms: 1193x + -139x = 1054x -94 + 1054x + -60x2 = 94 + 139x + -94 + -139x Reorder the terms: -94 + 1054x + -60x2 = 94 + -94 + 139x + -139x Combine like terms: 94 + -94 = 0 -94 + 1054x + -60x2 = 0 + 139x + -139x -94 + 1054x + -60x2 = 139x + -139x Combine like terms: 139x + -139x = 0 -94 + 1054x + -60x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + 527x + -30x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + 527x + -30x2)' equal to zero and attempt to solve: Simplifying -47 + 527x + -30x2 = 0 Solving -47 + 527x + -30x2 = 0 Begin completing the square. Divide all terms by -30 the coefficient of the squared term: Divide each side by '-30'. 1.566666667 + -17.56666667x + x2 = 0.0 Move the constant term to the right: Add '-1.566666667' to each side of the equation. 1.566666667 + -17.56666667x + -1.566666667 + x2 = 0.0 + -1.566666667 Reorder the terms: 1.566666667 + -1.566666667 + -17.56666667x + x2 = 0.0 + -1.566666667 Combine like terms: 1.566666667 + -1.566666667 = 0.000000000 0.000000000 + -17.56666667x + x2 = 0.0 + -1.566666667 -17.56666667x + x2 = 0.0 + -1.566666667 Combine like terms: 0.0 + -1.566666667 = -1.566666667 -17.56666667x + x2 = -1.566666667 The x term is -17.56666667x. Take half its coefficient (-8.783333335). Square it (77.14694447) and add it to both sides. Add '77.14694447' to each side of the equation. -17.56666667x + 77.14694447 + x2 = -1.566666667 + 77.14694447 Reorder the terms: 77.14694447 + -17.56666667x + x2 = -1.566666667 + 77.14694447 Combine like terms: -1.566666667 + 77.14694447 = 75.580277803 77.14694447 + -17.56666667x + x2 = 75.580277803 Factor a perfect square on the left side: (x + -8.783333335)(x + -8.783333335) = 75.580277803 Calculate the square root of the right side: 8.69369184 Break this problem into two subproblems by setting (x + -8.783333335) equal to 8.69369184 and -8.69369184.Subproblem 1
x + -8.783333335 = 8.69369184 Simplifying x + -8.783333335 = 8.69369184 Reorder the terms: -8.783333335 + x = 8.69369184 Solving -8.783333335 + x = 8.69369184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.783333335' to each side of the equation. -8.783333335 + 8.783333335 + x = 8.69369184 + 8.783333335 Combine like terms: -8.783333335 + 8.783333335 = 0.000000000 0.000000000 + x = 8.69369184 + 8.783333335 x = 8.69369184 + 8.783333335 Combine like terms: 8.69369184 + 8.783333335 = 17.477025175 x = 17.477025175 Simplifying x = 17.477025175Subproblem 2
x + -8.783333335 = -8.69369184 Simplifying x + -8.783333335 = -8.69369184 Reorder the terms: -8.783333335 + x = -8.69369184 Solving -8.783333335 + x = -8.69369184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.783333335' to each side of the equation. -8.783333335 + 8.783333335 + x = -8.69369184 + 8.783333335 Combine like terms: -8.783333335 + 8.783333335 = 0.000000000 0.000000000 + x = -8.69369184 + 8.783333335 x = -8.69369184 + 8.783333335 Combine like terms: -8.69369184 + 8.783333335 = 0.089641495 x = 0.089641495 Simplifying x = 0.089641495Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.477025175, 0.089641495}Solution
x = {17.477025175, 0.089641495}
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