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Simplifying x + -1x(225 + -5 + -5x) + 4 + -3x * 5 = 0 Combine like terms: 225 + -5 = 220 x + -1x(220 + -5x) + 4 + -3x * 5 = 0 x + (220 * -1x + -5x * -1x) + 4 + -3x * 5 = 0 x + (-220x + 5x2) + 4 + -3x * 5 = 0 Reorder the terms for easier multiplication: x + -220x + 5x2 + 4 + -3 * 5x = 0 Multiply -3 * 5 x + -220x + 5x2 + 4 + -15x = 0 Reorder the terms: 4 + x + -220x + -15x + 5x2 = 0 Combine like terms: x + -220x = -219x 4 + -219x + -15x + 5x2 = 0 Combine like terms: -219x + -15x = -234x 4 + -234x + 5x2 = 0 Solving 4 + -234x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -46.8x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -46.8x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -46.8x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -46.8x + x2 = 0 + -0.8 -46.8x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -46.8x + x2 = -0.8 The x term is -46.8x. Take half its coefficient (-23.4). Square it (547.56) and add it to both sides. Add '547.56' to each side of the equation. -46.8x + 547.56 + x2 = -0.8 + 547.56 Reorder the terms: 547.56 + -46.8x + x2 = -0.8 + 547.56 Combine like terms: -0.8 + 547.56 = 546.76 547.56 + -46.8x + x2 = 546.76 Factor a perfect square on the left side: (x + -23.4)(x + -23.4) = 546.76 Calculate the square root of the right side: 23.382899735 Break this problem into two subproblems by setting (x + -23.4) equal to 23.382899735 and -23.382899735.Subproblem 1
x + -23.4 = 23.382899735 Simplifying x + -23.4 = 23.382899735 Reorder the terms: -23.4 + x = 23.382899735 Solving -23.4 + x = 23.382899735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.4' to each side of the equation. -23.4 + 23.4 + x = 23.382899735 + 23.4 Combine like terms: -23.4 + 23.4 = 0.0 0.0 + x = 23.382899735 + 23.4 x = 23.382899735 + 23.4 Combine like terms: 23.382899735 + 23.4 = 46.782899735 x = 46.782899735 Simplifying x = 46.782899735Subproblem 2
x + -23.4 = -23.382899735 Simplifying x + -23.4 = -23.382899735 Reorder the terms: -23.4 + x = -23.382899735 Solving -23.4 + x = -23.382899735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.4' to each side of the equation. -23.4 + 23.4 + x = -23.382899735 + 23.4 Combine like terms: -23.4 + 23.4 = 0.0 0.0 + x = -23.382899735 + 23.4 x = -23.382899735 + 23.4 Combine like terms: -23.382899735 + 23.4 = 0.017100265 x = 0.017100265 Simplifying x = 0.017100265Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.782899735, 0.017100265}
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