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Simplifying 5x2 + 8x = 660 Reorder the terms: 8x + 5x2 = 660 Solving 8x + 5x2 = 660 Solving for variable 'x'. Reorder the terms: -660 + 8x + 5x2 = 660 + -660 Combine like terms: 660 + -660 = 0 -660 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -132 + 1.6x + x2 = 0 Move the constant term to the right: Add '132' to each side of the equation. -132 + 1.6x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + 1.6x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + 1.6x + x2 = 0 + 132 1.6x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 1.6x + x2 = 132 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 132 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 132 + 0.64 Combine like terms: 132 + 0.64 = 132.64 0.64 + 1.6x + x2 = 132.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 132.64 Calculate the square root of the right side: 11.516944039 Break this problem into two subproblems by setting (x + 0.8) equal to 11.516944039 and -11.516944039.Subproblem 1
x + 0.8 = 11.516944039 Simplifying x + 0.8 = 11.516944039 Reorder the terms: 0.8 + x = 11.516944039 Solving 0.8 + x = 11.516944039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 11.516944039 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 11.516944039 + -0.8 x = 11.516944039 + -0.8 Combine like terms: 11.516944039 + -0.8 = 10.716944039 x = 10.716944039 Simplifying x = 10.716944039Subproblem 2
x + 0.8 = -11.516944039 Simplifying x + 0.8 = -11.516944039 Reorder the terms: 0.8 + x = -11.516944039 Solving 0.8 + x = -11.516944039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -11.516944039 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -11.516944039 + -0.8 x = -11.516944039 + -0.8 Combine like terms: -11.516944039 + -0.8 = -12.316944039 x = -12.316944039 Simplifying x = -12.316944039Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.716944039, -12.316944039}
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