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Simplifying 8x2 + 10x = 1440 Reorder the terms: 10x + 8x2 = 1440 Solving 10x + 8x2 = 1440 Solving for variable 'x'. Reorder the terms: -1440 + 10x + 8x2 = 1440 + -1440 Combine like terms: 1440 + -1440 = 0 -1440 + 10x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-720 + 5x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-720 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying -720 + 5x + 4x2 = 0 Solving -720 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -180 + 1.25x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 1.25x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 1.25x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 1.25x + x2 = 0 + 180 1.25x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 1.25x + x2 = 180 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 180 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 180 + 0.390625 Combine like terms: 180 + 0.390625 = 180.390625 0.390625 + 1.25x + x2 = 180.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 180.390625 Calculate the square root of the right side: 13.43095771 Break this problem into two subproblems by setting (x + 0.625) equal to 13.43095771 and -13.43095771.Subproblem 1
x + 0.625 = 13.43095771 Simplifying x + 0.625 = 13.43095771 Reorder the terms: 0.625 + x = 13.43095771 Solving 0.625 + x = 13.43095771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 13.43095771 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 13.43095771 + -0.625 x = 13.43095771 + -0.625 Combine like terms: 13.43095771 + -0.625 = 12.80595771 x = 12.80595771 Simplifying x = 12.80595771Subproblem 2
x + 0.625 = -13.43095771 Simplifying x + 0.625 = -13.43095771 Reorder the terms: 0.625 + x = -13.43095771 Solving 0.625 + x = -13.43095771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -13.43095771 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -13.43095771 + -0.625 x = -13.43095771 + -0.625 Combine like terms: -13.43095771 + -0.625 = -14.05595771 x = -14.05595771 Simplifying x = -14.05595771Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.80595771, -14.05595771}Solution
x = {12.80595771, -14.05595771}
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