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Simplifying -16x2 + 40x + 400 = 0 Reorder the terms: 400 + 40x + -16x2 = 0 Solving 400 + 40x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(50 + 5x + -2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(50 + 5x + -2x2)' equal to zero and attempt to solve: Simplifying 50 + 5x + -2x2 = 0 Solving 50 + 5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -25 + -2.5x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -2.5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -2.5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -2.5x + x2 = 0 + 25 -2.5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -2.5x + x2 = 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 = 25 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 25 + 1.5625 Combine like terms: 25 + 1.5625 = 26.5625 1.5625 + -2.5x + x2 = 26.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (x + -1.25) equal to 5.153882032 and -5.153882032.Subproblem 1
x + -1.25 = 5.153882032 Simplifying x + -1.25 = 5.153882032 Reorder the terms: -1.25 + x = 5.153882032 Solving -1.25 + x = 5.153882032 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 = 5.153882032 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 5.153882032 + 1.25 x = 5.153882032 + 1.25 Combine like terms: 5.153882032 + 1.25 = 6.403882032 x = 6.403882032 Simplifying x = 6.403882032Subproblem 2
x + -1.25 = -5.153882032 Simplifying x + -1.25 = -5.153882032 Reorder the terms: -1.25 + x = -5.153882032 Solving -1.25 + x = -5.153882032 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 = -5.153882032 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -5.153882032 + 1.25 x = -5.153882032 + 1.25 Combine like terms: -5.153882032 + 1.25 = -3.903882032 x = -3.903882032 Simplifying x = -3.903882032Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.403882032, -3.903882032}Solution
x = {6.403882032, -3.903882032}
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