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Simplifying 30x = 2x2 + -16 Reorder the terms: 30x = -16 + 2x2 Solving 30x = -16 + 2x2 Solving for variable 'x'. Reorder the terms: 16 + 30x + -2x2 = -16 + 2x2 + 16 + -2x2 Reorder the terms: 16 + 30x + -2x2 = -16 + 16 + 2x2 + -2x2 Combine like terms: -16 + 16 = 0 16 + 30x + -2x2 = 0 + 2x2 + -2x2 16 + 30x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 16 + 30x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 15x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + 15x + -1x2)' equal to zero and attempt to solve: Simplifying 8 + 15x + -1x2 = 0 Solving 8 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -15x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -15x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -15x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -15x + x2 = 0 + 8 -15x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -15x + x2 = 8 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 8 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 8 + 56.25 Combine like terms: 8 + 56.25 = 64.25 56.25 + -15x + x2 = 64.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + -7.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + -7.5 = 8.015609771 Simplifying x + -7.5 = 8.015609771 Reorder the terms: -7.5 + x = 8.015609771 Solving -7.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.015609771 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.015609771 + 7.5 x = 8.015609771 + 7.5 Combine like terms: 8.015609771 + 7.5 = 15.515609771 x = 15.515609771 Simplifying x = 15.515609771Subproblem 2
x + -7.5 = -8.015609771 Simplifying x + -7.5 = -8.015609771 Reorder the terms: -7.5 + x = -8.015609771 Solving -7.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.015609771 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.015609771 + 7.5 x = -8.015609771 + 7.5 Combine like terms: -8.015609771 + 7.5 = -0.515609771 x = -0.515609771 Simplifying x = -0.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.515609771, -0.515609771}Solution
x = {15.515609771, -0.515609771}
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