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Simplifying 0.5(1x + -6) + 1 = 2x(1x + -10) + -3 Reorder the terms: 0.5(-6 + 1x) + 1 = 2x(1x + -10) + -3 (-6 * 0.5 + 1x * 0.5) + 1 = 2x(1x + -10) + -3 (-3 + 0.5x) + 1 = 2x(1x + -10) + -3 Reorder the terms: -3 + 1 + 0.5x = 2x(1x + -10) + -3 Combine like terms: -3 + 1 = -2 -2 + 0.5x = 2x(1x + -10) + -3 Reorder the terms: -2 + 0.5x = 2x(-10 + 1x) + -3 -2 + 0.5x = (-10 * 2x + 1x * 2x) + -3 -2 + 0.5x = (-20x + 2x2) + -3 Reorder the terms: -2 + 0.5x = -3 + -20x + 2x2 Solving -2 + 0.5x = -3 + -20x + 2x2 Solving for variable 'x'. Reorder the terms: -2 + 3 + 0.5x + 20x + -2x2 = -3 + -20x + 2x2 + 3 + 20x + -2x2 Combine like terms: -2 + 3 = 1 1 + 0.5x + 20x + -2x2 = -3 + -20x + 2x2 + 3 + 20x + -2x2 Combine like terms: 0.5x + 20x = 20.5x 1 + 20.5x + -2x2 = -3 + -20x + 2x2 + 3 + 20x + -2x2 Reorder the terms: 1 + 20.5x + -2x2 = -3 + 3 + -20x + 20x + 2x2 + -2x2 Combine like terms: -3 + 3 = 0 1 + 20.5x + -2x2 = 0 + -20x + 20x + 2x2 + -2x2 1 + 20.5x + -2x2 = -20x + 20x + 2x2 + -2x2 Combine like terms: -20x + 20x = 0 1 + 20.5x + -2x2 = 0 + 2x2 + -2x2 1 + 20.5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1 + 20.5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -10.25x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -10.25x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -10.25x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -10.25x + x2 = 0 + 0.5 -10.25x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -10.25x + x2 = 0.5 The x term is -10.25x. Take half its coefficient (-5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. -10.25x + 26.265625 + x2 = 0.5 + 26.265625 Reorder the terms: 26.265625 + -10.25x + x2 = 0.5 + 26.265625 Combine like terms: 0.5 + 26.265625 = 26.765625 26.265625 + -10.25x + x2 = 26.765625 Factor a perfect square on the left side: (x + -5.125)(x + -5.125) = 26.765625 Calculate the square root of the right side: 5.173550522 Break this problem into two subproblems by setting (x + -5.125) equal to 5.173550522 and -5.173550522.Subproblem 1
x + -5.125 = 5.173550522 Simplifying x + -5.125 = 5.173550522 Reorder the terms: -5.125 + x = 5.173550522 Solving -5.125 + x = 5.173550522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = 5.173550522 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 5.173550522 + 5.125 x = 5.173550522 + 5.125 Combine like terms: 5.173550522 + 5.125 = 10.298550522 x = 10.298550522 Simplifying x = 10.298550522Subproblem 2
x + -5.125 = -5.173550522 Simplifying x + -5.125 = -5.173550522 Reorder the terms: -5.125 + x = -5.173550522 Solving -5.125 + x = -5.173550522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = -5.173550522 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -5.173550522 + 5.125 x = -5.173550522 + 5.125 Combine like terms: -5.173550522 + 5.125 = -0.048550522 x = -0.048550522 Simplifying x = -0.048550522Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.298550522, -0.048550522}
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