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Simplifying 0 = 16x2 + 200x + 15 Reorder the terms: 0 = 15 + 200x + 16x2 Solving 0 = 15 + 200x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + -200x + -16x2 = 15 + 200x + 16x2 + -15 + -200x + -16x2 Reorder the terms: -15 + -200x + -16x2 = 15 + -15 + 200x + -200x + 16x2 + -16x2 Combine like terms: 15 + -15 = 0 -15 + -200x + -16x2 = 0 + 200x + -200x + 16x2 + -16x2 -15 + -200x + -16x2 = 200x + -200x + 16x2 + -16x2 Combine like terms: 200x + -200x = 0 -15 + -200x + -16x2 = 0 + 16x2 + -16x2 -15 + -200x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -15 + -200x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 200x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 200x + 16x2)' equal to zero and attempt to solve: Simplifying 15 + 200x + 16x2 = 0 Solving 15 + 200x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.9375 + 12.5x + x2 = 0 Move the constant term to the right: Add '-0.9375' to each side of the equation. 0.9375 + 12.5x + -0.9375 + x2 = 0 + -0.9375 Reorder the terms: 0.9375 + -0.9375 + 12.5x + x2 = 0 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + 12.5x + x2 = 0 + -0.9375 12.5x + x2 = 0 + -0.9375 Combine like terms: 0 + -0.9375 = -0.9375 12.5x + x2 = -0.9375 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = -0.9375 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = -0.9375 + 39.0625 Combine like terms: -0.9375 + 39.0625 = 38.125 39.0625 + 12.5x + x2 = 38.125 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 38.125 Calculate the square root of the right side: 6.174544518 Break this problem into two subproblems by setting (x + 6.25) equal to 6.174544518 and -6.174544518.Subproblem 1
x + 6.25 = 6.174544518 Simplifying x + 6.25 = 6.174544518 Reorder the terms: 6.25 + x = 6.174544518 Solving 6.25 + x = 6.174544518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 6.174544518 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 6.174544518 + -6.25 x = 6.174544518 + -6.25 Combine like terms: 6.174544518 + -6.25 = -0.075455482 x = -0.075455482 Simplifying x = -0.075455482Subproblem 2
x + 6.25 = -6.174544518 Simplifying x + 6.25 = -6.174544518 Reorder the terms: 6.25 + x = -6.174544518 Solving 6.25 + x = -6.174544518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -6.174544518 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -6.174544518 + -6.25 x = -6.174544518 + -6.25 Combine like terms: -6.174544518 + -6.25 = -12.424544518 x = -12.424544518 Simplifying x = -12.424544518Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.075455482, -12.424544518}Solution
x = {-0.075455482, -12.424544518}
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