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Simplifying -9 = 4x2 + 16x Reorder the terms: -9 = 16x + 4x2 Solving -9 = 16x + 4x2 Solving for variable 'x'. Reorder the terms: -9 + -16x + -4x2 = 16x + -16x + 4x2 + -4x2 Combine like terms: 16x + -16x = 0 -9 + -16x + -4x2 = 0 + 4x2 + -4x2 -9 + -16x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -9 + -16x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 16x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 16x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + 16x + 4x2 = 0 Solving 9 + 16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 4x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 4x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 4x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 4x + x2 = 0 + -2.25 4x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 4x + x2 = -2.25 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -2.25 + 4 Reorder the terms: 4 + 4x + x2 = -2.25 + 4 Combine like terms: -2.25 + 4 = 1.75 4 + 4x + x2 = 1.75 Factor a perfect square on the left side: (x + 2)(x + 2) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + 2) equal to 1.322875656 and -1.322875656.Subproblem 1
x + 2 = 1.322875656 Simplifying x + 2 = 1.322875656 Reorder the terms: 2 + x = 1.322875656 Solving 2 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.322875656 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.322875656 + -2 x = 1.322875656 + -2 Combine like terms: 1.322875656 + -2 = -0.677124344 x = -0.677124344 Simplifying x = -0.677124344Subproblem 2
x + 2 = -1.322875656 Simplifying x + 2 = -1.322875656 Reorder the terms: 2 + x = -1.322875656 Solving 2 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.322875656 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.322875656 + -2 x = -1.322875656 + -2 Combine like terms: -1.322875656 + -2 = -3.322875656 x = -3.322875656 Simplifying x = -3.322875656Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.677124344, -3.322875656}Solution
x = {-0.677124344, -3.322875656}
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