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Simplifying -4x(2x + 7) = 2x + -18 Reorder the terms: -4x(7 + 2x) = 2x + -18 (7 * -4x + 2x * -4x) = 2x + -18 (-28x + -8x2) = 2x + -18 Reorder the terms: -28x + -8x2 = -18 + 2x Solving -28x + -8x2 = -18 + 2x Solving for variable 'x'. Reorder the terms: 18 + -28x + -2x + -8x2 = -18 + 2x + 18 + -2x Combine like terms: -28x + -2x = -30x 18 + -30x + -8x2 = -18 + 2x + 18 + -2x Reorder the terms: 18 + -30x + -8x2 = -18 + 18 + 2x + -2x Combine like terms: -18 + 18 = 0 18 + -30x + -8x2 = 0 + 2x + -2x 18 + -30x + -8x2 = 2x + -2x Combine like terms: 2x + -2x = 0 18 + -30x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -15x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -15x + -4x2)' equal to zero and attempt to solve: Simplifying 9 + -15x + -4x2 = 0 Solving 9 + -15x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.25 + 3.75x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 3.75x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 3.75x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 3.75x + x2 = 0 + 2.25 3.75x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 3.75x + x2 = 2.25 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 2.25 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 2.25 + 3.515625 Combine like terms: 2.25 + 3.515625 = 5.765625 3.515625 + 3.75x + x2 = 5.765625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 5.765625 Calculate the square root of the right side: 2.401171589 Break this problem into two subproblems by setting (x + 1.875) equal to 2.401171589 and -2.401171589.Subproblem 1
x + 1.875 = 2.401171589 Simplifying x + 1.875 = 2.401171589 Reorder the terms: 1.875 + x = 2.401171589 Solving 1.875 + x = 2.401171589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 2.401171589 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 2.401171589 + -1.875 x = 2.401171589 + -1.875 Combine like terms: 2.401171589 + -1.875 = 0.526171589 x = 0.526171589 Simplifying x = 0.526171589Subproblem 2
x + 1.875 = -2.401171589 Simplifying x + 1.875 = -2.401171589 Reorder the terms: 1.875 + x = -2.401171589 Solving 1.875 + x = -2.401171589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -2.401171589 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -2.401171589 + -1.875 x = -2.401171589 + -1.875 Combine like terms: -2.401171589 + -1.875 = -4.276171589 x = -4.276171589 Simplifying x = -4.276171589Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.526171589, -4.276171589}Solution
x = {0.526171589, -4.276171589}
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