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Simplifying 2 = -16x2 + 20x + 300 Reorder the terms: 2 = 300 + 20x + -16x2 Solving 2 = 300 + 20x + -16x2 Solving for variable 'x'. Combine like terms: 2 + -300 = -298 -298 + -20x + 16x2 = 300 + 20x + -16x2 + -300 + -20x + 16x2 Reorder the terms: -298 + -20x + 16x2 = 300 + -300 + 20x + -20x + -16x2 + 16x2 Combine like terms: 300 + -300 = 0 -298 + -20x + 16x2 = 0 + 20x + -20x + -16x2 + 16x2 -298 + -20x + 16x2 = 20x + -20x + -16x2 + 16x2 Combine like terms: 20x + -20x = 0 -298 + -20x + 16x2 = 0 + -16x2 + 16x2 -298 + -20x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -298 + -20x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-149 + -10x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-149 + -10x + 8x2)' equal to zero and attempt to solve: Simplifying -149 + -10x + 8x2 = 0 Solving -149 + -10x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -18.625 + -1.25x + x2 = 0 Move the constant term to the right: Add '18.625' to each side of the equation. -18.625 + -1.25x + 18.625 + x2 = 0 + 18.625 Reorder the terms: -18.625 + 18.625 + -1.25x + x2 = 0 + 18.625 Combine like terms: -18.625 + 18.625 = 0.000 0.000 + -1.25x + x2 = 0 + 18.625 -1.25x + x2 = 0 + 18.625 Combine like terms: 0 + 18.625 = 18.625 -1.25x + x2 = 18.625 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 = 18.625 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 18.625 + 0.390625 Combine like terms: 18.625 + 0.390625 = 19.015625 0.390625 + -1.25x + x2 = 19.015625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 19.015625 Calculate the square root of the right side: 4.360690886 Break this problem into two subproblems by setting (x + -0.625) equal to 4.360690886 and -4.360690886.Subproblem 1
x + -0.625 = 4.360690886 Simplifying x + -0.625 = 4.360690886 Reorder the terms: -0.625 + x = 4.360690886 Solving -0.625 + x = 4.360690886 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 = 4.360690886 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 4.360690886 + 0.625 x = 4.360690886 + 0.625 Combine like terms: 4.360690886 + 0.625 = 4.985690886 x = 4.985690886 Simplifying x = 4.985690886Subproblem 2
x + -0.625 = -4.360690886 Simplifying x + -0.625 = -4.360690886 Reorder the terms: -0.625 + x = -4.360690886 Solving -0.625 + x = -4.360690886 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 = -4.360690886 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -4.360690886 + 0.625 x = -4.360690886 + 0.625 Combine like terms: -4.360690886 + 0.625 = -3.735690886 x = -3.735690886 Simplifying x = -3.735690886Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.985690886, -3.735690886}Solution
x = {4.985690886, -3.735690886}
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