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Simplifying -16x2 + 200 = 20x Reorder the terms: 200 + -16x2 = 20x Solving 200 + -16x2 = 20x Solving for variable 'x'. Reorder the terms: 200 + -20x + -16x2 = 20x + -20x Combine like terms: 20x + -20x = 0 200 + -20x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(50 + -5x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(50 + -5x + -4x2)' equal to zero and attempt to solve: Simplifying 50 + -5x + -4x2 = 0 Solving 50 + -5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -12.5 + 1.25x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 1.25x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 1.25x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 1.25x + x2 = 0 + 12.5 1.25x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 1.25x + x2 = 12.5 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 = 12.5 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 12.5 + 0.390625 Combine like terms: 12.5 + 0.390625 = 12.890625 0.390625 + 1.25x + x2 = 12.890625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 12.890625 Calculate the square root of the right side: 3.590351654 Break this problem into two subproblems by setting (x + 0.625) equal to 3.590351654 and -3.590351654.Subproblem 1
x + 0.625 = 3.590351654 Simplifying x + 0.625 = 3.590351654 Reorder the terms: 0.625 + x = 3.590351654 Solving 0.625 + x = 3.590351654 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 = 3.590351654 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 3.590351654 + -0.625 x = 3.590351654 + -0.625 Combine like terms: 3.590351654 + -0.625 = 2.965351654 x = 2.965351654 Simplifying x = 2.965351654Subproblem 2
x + 0.625 = -3.590351654 Simplifying x + 0.625 = -3.590351654 Reorder the terms: 0.625 + x = -3.590351654 Solving 0.625 + x = -3.590351654 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 = -3.590351654 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -3.590351654 + -0.625 x = -3.590351654 + -0.625 Combine like terms: -3.590351654 + -0.625 = -4.215351654 x = -4.215351654 Simplifying x = -4.215351654Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.965351654, -4.215351654}Solution
x = {2.965351654, -4.215351654}
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