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Simplifying 0 = -16x2 + 24x + 6 Reorder the terms: 0 = 6 + 24x + -16x2 Solving 0 = 6 + 24x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -24x + 16x2 = 6 + 24x + -16x2 + -6 + -24x + 16x2 Reorder the terms: -6 + -24x + 16x2 = 6 + -6 + 24x + -24x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -6 + -24x + 16x2 = 0 + 24x + -24x + -16x2 + 16x2 -6 + -24x + 16x2 = 24x + -24x + -16x2 + 16x2 Combine like terms: 24x + -24x = 0 -6 + -24x + 16x2 = 0 + -16x2 + 16x2 -6 + -24x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -6 + -24x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -12x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -12x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + -12x + 8x2 = 0 Solving -3 + -12x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -1.5x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -1.5x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -1.5x + x2 = 0 + 0.375 -1.5x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -1.5x + x2 = 0.375 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.375 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.375 + 0.5625 Combine like terms: 0.375 + 0.5625 = 0.9375 0.5625 + -1.5x + x2 = 0.9375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.9375 Calculate the square root of the right side: 0.968245837 Break this problem into two subproblems by setting (x + -0.75) equal to 0.968245837 and -0.968245837.Subproblem 1
x + -0.75 = 0.968245837 Simplifying x + -0.75 = 0.968245837 Reorder the terms: -0.75 + x = 0.968245837 Solving -0.75 + x = 0.968245837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.968245837 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.968245837 + 0.75 x = 0.968245837 + 0.75 Combine like terms: 0.968245837 + 0.75 = 1.718245837 x = 1.718245837 Simplifying x = 1.718245837Subproblem 2
x + -0.75 = -0.968245837 Simplifying x + -0.75 = -0.968245837 Reorder the terms: -0.75 + x = -0.968245837 Solving -0.75 + x = -0.968245837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.968245837 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.968245837 + 0.75 x = -0.968245837 + 0.75 Combine like terms: -0.968245837 + 0.75 = -0.218245837 x = -0.218245837 Simplifying x = -0.218245837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.718245837, -0.218245837}Solution
x = {1.718245837, -0.218245837}
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