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Simplifying 0 = -16x2 + 40x + 4 Reorder the terms: 0 = 4 + 40x + -16x2 Solving 0 = 4 + 40x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -40x + 16x2 = 4 + 40x + -16x2 + -4 + -40x + 16x2 Reorder the terms: -4 + -40x + 16x2 = 4 + -4 + 40x + -40x + -16x2 + 16x2 Combine like terms: 4 + -4 = 0 -4 + -40x + 16x2 = 0 + 40x + -40x + -16x2 + 16x2 -4 + -40x + 16x2 = 40x + -40x + -16x2 + 16x2 Combine like terms: 40x + -40x = 0 -4 + -40x + 16x2 = 0 + -16x2 + 16x2 -4 + -40x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -4 + -40x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -10x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -10x + 4x2)' equal to zero and attempt to solve: Simplifying -1 + -10x + 4x2 = 0 Solving -1 + -10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -2.5x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.5x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.5x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.5x + x2 = 0 + 0.25 -2.5x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.5x + x2 = 0.25 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 0.25 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 0.25 + 1.5625 Combine like terms: 0.25 + 1.5625 = 1.8125 1.5625 + -2.5x + x2 = 1.8125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (x + -1.25) equal to 1.346291202 and -1.346291202.Subproblem 1
x + -1.25 = 1.346291202 Simplifying x + -1.25 = 1.346291202 Reorder the terms: -1.25 + x = 1.346291202 Solving -1.25 + x = 1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.346291202 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.346291202 + 1.25 x = 1.346291202 + 1.25 Combine like terms: 1.346291202 + 1.25 = 2.596291202 x = 2.596291202 Simplifying x = 2.596291202Subproblem 2
x + -1.25 = -1.346291202 Simplifying x + -1.25 = -1.346291202 Reorder the terms: -1.25 + x = -1.346291202 Solving -1.25 + x = -1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.346291202 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.346291202 + 1.25 x = -1.346291202 + 1.25 Combine like terms: -1.346291202 + 1.25 = -0.096291202 x = -0.096291202 Simplifying x = -0.096291202Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.596291202, -0.096291202}Solution
x = {2.596291202, -0.096291202}
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