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Simplifying 0 = 4x2 + -30x + 8 Reorder the terms: 0 = 8 + -30x + 4x2 Solving 0 = 8 + -30x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + 30x + -4x2 = 8 + -30x + 4x2 + -8 + 30x + -4x2 Reorder the terms: -8 + 30x + -4x2 = 8 + -8 + -30x + 30x + 4x2 + -4x2 Combine like terms: 8 + -8 = 0 -8 + 30x + -4x2 = 0 + -30x + 30x + 4x2 + -4x2 -8 + 30x + -4x2 = -30x + 30x + 4x2 + -4x2 Combine like terms: -30x + 30x = 0 -8 + 30x + -4x2 = 0 + 4x2 + -4x2 -8 + 30x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -8 + 30x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 15x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 15x + -2x2)' equal to zero and attempt to solve: Simplifying -4 + 15x + -2x2 = 0 Solving -4 + 15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2 + -7.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -7.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -7.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7.5x + x2 = 0 + -2 -7.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -7.5x + x2 = -2 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -2 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -2 + 14.0625 Combine like terms: -2 + 14.0625 = 12.0625 14.0625 + -7.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + -3.75) equal to 3.473110997 and -3.473110997.Subproblem 1
x + -3.75 = 3.473110997 Simplifying x + -3.75 = 3.473110997 Reorder the terms: -3.75 + x = 3.473110997 Solving -3.75 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 3.473110997 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 3.473110997 + 3.75 x = 3.473110997 + 3.75 Combine like terms: 3.473110997 + 3.75 = 7.223110997 x = 7.223110997 Simplifying x = 7.223110997Subproblem 2
x + -3.75 = -3.473110997 Simplifying x + -3.75 = -3.473110997 Reorder the terms: -3.75 + x = -3.473110997 Solving -3.75 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -3.473110997 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -3.473110997 + 3.75 x = -3.473110997 + 3.75 Combine like terms: -3.473110997 + 3.75 = 0.276889003 x = 0.276889003 Simplifying x = 0.276889003Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.223110997, 0.276889003}Solution
x = {7.223110997, 0.276889003}
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