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Simplifying 56 = -16x2 + 62x + 4 Reorder the terms: 56 = 4 + 62x + -16x2 Solving 56 = 4 + 62x + -16x2 Solving for variable 'x'. Combine like terms: 56 + -4 = 52 52 + -62x + 16x2 = 4 + 62x + -16x2 + -4 + -62x + 16x2 Reorder the terms: 52 + -62x + 16x2 = 4 + -4 + 62x + -62x + -16x2 + 16x2 Combine like terms: 4 + -4 = 0 52 + -62x + 16x2 = 0 + 62x + -62x + -16x2 + 16x2 52 + -62x + 16x2 = 62x + -62x + -16x2 + 16x2 Combine like terms: 62x + -62x = 0 52 + -62x + 16x2 = 0 + -16x2 + 16x2 52 + -62x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 52 + -62x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(26 + -31x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(26 + -31x + 8x2)' equal to zero and attempt to solve: Simplifying 26 + -31x + 8x2 = 0 Solving 26 + -31x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.25 + -3.875x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -3.875x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -3.875x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -3.875x + x2 = 0 + -3.25 -3.875x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -3.875x + x2 = -3.25 The x term is -3.875x. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875x + 3.75390625 + x2 = -3.25 + 3.75390625 Reorder the terms: 3.75390625 + -3.875x + x2 = -3.25 + 3.75390625 Combine like terms: -3.25 + 3.75390625 = 0.50390625 3.75390625 + -3.875x + x2 = 0.50390625 Factor a perfect square on the left side: (x + -1.9375)(x + -1.9375) = 0.50390625 Calculate the square root of the right side: 0.709863543 Break this problem into two subproblems by setting (x + -1.9375) equal to 0.709863543 and -0.709863543.Subproblem 1
x + -1.9375 = 0.709863543 Simplifying x + -1.9375 = 0.709863543 Reorder the terms: -1.9375 + x = 0.709863543 Solving -1.9375 + x = 0.709863543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + x = 0.709863543 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + x = 0.709863543 + 1.9375 x = 0.709863543 + 1.9375 Combine like terms: 0.709863543 + 1.9375 = 2.647363543 x = 2.647363543 Simplifying x = 2.647363543Subproblem 2
x + -1.9375 = -0.709863543 Simplifying x + -1.9375 = -0.709863543 Reorder the terms: -1.9375 + x = -0.709863543 Solving -1.9375 + x = -0.709863543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + x = -0.709863543 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + x = -0.709863543 + 1.9375 x = -0.709863543 + 1.9375 Combine like terms: -0.709863543 + 1.9375 = 1.227636457 x = 1.227636457 Simplifying x = 1.227636457Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.647363543, 1.227636457}Solution
x = {2.647363543, 1.227636457}
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