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Simplifying 900 + 20x + -16x2 = 0 Solving 900 + 20x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(225 + 5x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(225 + 5x + -4x2)' equal to zero and attempt to solve: Simplifying 225 + 5x + -4x2 = 0 Solving 225 + 5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -56.25 + -1.25x + x2 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + -1.25x + 56.25 + x2 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + -1.25x + x2 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + -1.25x + x2 = 0 + 56.25 -1.25x + x2 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 -1.25x + x2 = 56.25 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 = 56.25 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 56.25 + 0.390625 Combine like terms: 56.25 + 0.390625 = 56.640625 0.390625 + -1.25x + x2 = 56.640625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 56.640625 Calculate the square root of the right side: 7.525996612 Break this problem into two subproblems by setting (x + -0.625) equal to 7.525996612 and -7.525996612.Subproblem 1
x + -0.625 = 7.525996612 Simplifying x + -0.625 = 7.525996612 Reorder the terms: -0.625 + x = 7.525996612 Solving -0.625 + x = 7.525996612 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 = 7.525996612 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 7.525996612 + 0.625 x = 7.525996612 + 0.625 Combine like terms: 7.525996612 + 0.625 = 8.150996612 x = 8.150996612 Simplifying x = 8.150996612Subproblem 2
x + -0.625 = -7.525996612 Simplifying x + -0.625 = -7.525996612 Reorder the terms: -0.625 + x = -7.525996612 Solving -0.625 + x = -7.525996612 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 = -7.525996612 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -7.525996612 + 0.625 x = -7.525996612 + 0.625 Combine like terms: -7.525996612 + 0.625 = -6.900996612 x = -6.900996612 Simplifying x = -6.900996612Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.150996612, -6.900996612}Solution
x = {8.150996612, -6.900996612}
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