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Simplifying -16x2 + 20x + 40 = 0 Reorder the terms: 40 + 20x + -16x2 = 0 Solving 40 + 20x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(10 + 5x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(10 + 5x + -4x2)' equal to zero and attempt to solve: Simplifying 10 + 5x + -4x2 = 0 Solving 10 + 5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.5 + -1.25x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -1.25x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -1.25x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -1.25x + x2 = 0 + 2.5 -1.25x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -1.25x + x2 = 2.5 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 = 2.5 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 2.5 + 0.390625 Combine like terms: 2.5 + 0.390625 = 2.890625 0.390625 + -1.25x + x2 = 2.890625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (x + -0.625) equal to 1.700183814 and -1.700183814.Subproblem 1
x + -0.625 = 1.700183814 Simplifying x + -0.625 = 1.700183814 Reorder the terms: -0.625 + x = 1.700183814 Solving -0.625 + x = 1.700183814 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 = 1.700183814 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.700183814 + 0.625 x = 1.700183814 + 0.625 Combine like terms: 1.700183814 + 0.625 = 2.325183814 x = 2.325183814 Simplifying x = 2.325183814Subproblem 2
x + -0.625 = -1.700183814 Simplifying x + -0.625 = -1.700183814 Reorder the terms: -0.625 + x = -1.700183814 Solving -0.625 + x = -1.700183814 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 = -1.700183814 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.700183814 + 0.625 x = -1.700183814 + 0.625 Combine like terms: -1.700183814 + 0.625 = -1.075183814 x = -1.075183814 Simplifying x = -1.075183814Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.325183814, -1.075183814}Solution
x = {2.325183814, -1.075183814}
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