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Simplifying 16x2 + -20x = 62 Reorder the terms: -20x + 16x2 = 62 Solving -20x + 16x2 = 62 Solving for variable 'x'. Reorder the terms: -62 + -20x + 16x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -62 + -20x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-31 + -10x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-31 + -10x + 8x2)' equal to zero and attempt to solve: Simplifying -31 + -10x + 8x2 = 0 Solving -31 + -10x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.875 + -1.25x + x2 = 0 Move the constant term to the right: Add '3.875' to each side of the equation. -3.875 + -1.25x + 3.875 + x2 = 0 + 3.875 Reorder the terms: -3.875 + 3.875 + -1.25x + x2 = 0 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + -1.25x + x2 = 0 + 3.875 -1.25x + x2 = 0 + 3.875 Combine like terms: 0 + 3.875 = 3.875 -1.25x + x2 = 3.875 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 = 3.875 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 3.875 + 0.390625 Combine like terms: 3.875 + 0.390625 = 4.265625 0.390625 + -1.25x + x2 = 4.265625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 4.265625 Calculate the square root of the right side: 2.065338955 Break this problem into two subproblems by setting (x + -0.625) equal to 2.065338955 and -2.065338955.Subproblem 1
x + -0.625 = 2.065338955 Simplifying x + -0.625 = 2.065338955 Reorder the terms: -0.625 + x = 2.065338955 Solving -0.625 + x = 2.065338955 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 = 2.065338955 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.065338955 + 0.625 x = 2.065338955 + 0.625 Combine like terms: 2.065338955 + 0.625 = 2.690338955 x = 2.690338955 Simplifying x = 2.690338955Subproblem 2
x + -0.625 = -2.065338955 Simplifying x + -0.625 = -2.065338955 Reorder the terms: -0.625 + x = -2.065338955 Solving -0.625 + x = -2.065338955 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 = -2.065338955 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.065338955 + 0.625 x = -2.065338955 + 0.625 Combine like terms: -2.065338955 + 0.625 = -1.440338955 x = -1.440338955 Simplifying x = -1.440338955Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.690338955, -1.440338955}Solution
x = {2.690338955, -1.440338955}
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