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Simplifying -2x2 + -11x + 24 = 6x2 + 17x + -28 Reorder the terms: 24 + -11x + -2x2 = 6x2 + 17x + -28 Reorder the terms: 24 + -11x + -2x2 = -28 + 17x + 6x2 Solving 24 + -11x + -2x2 = -28 + 17x + 6x2 Solving for variable 'x'. Reorder the terms: 24 + 28 + -11x + -17x + -2x2 + -6x2 = -28 + 17x + 6x2 + 28 + -17x + -6x2 Combine like terms: 24 + 28 = 52 52 + -11x + -17x + -2x2 + -6x2 = -28 + 17x + 6x2 + 28 + -17x + -6x2 Combine like terms: -11x + -17x = -28x 52 + -28x + -2x2 + -6x2 = -28 + 17x + 6x2 + 28 + -17x + -6x2 Combine like terms: -2x2 + -6x2 = -8x2 52 + -28x + -8x2 = -28 + 17x + 6x2 + 28 + -17x + -6x2 Reorder the terms: 52 + -28x + -8x2 = -28 + 28 + 17x + -17x + 6x2 + -6x2 Combine like terms: -28 + 28 = 0 52 + -28x + -8x2 = 0 + 17x + -17x + 6x2 + -6x2 52 + -28x + -8x2 = 17x + -17x + 6x2 + -6x2 Combine like terms: 17x + -17x = 0 52 + -28x + -8x2 = 0 + 6x2 + -6x2 52 + -28x + -8x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 52 + -28x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(13 + -7x + -2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(13 + -7x + -2x2)' equal to zero and attempt to solve: Simplifying 13 + -7x + -2x2 = 0 Solving 13 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 3.5x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 3.5x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 3.5x + x2 = 0 + 6.5 3.5x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 3.5x + x2 = 6.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 6.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 6.5 + 3.0625 Combine like terms: 6.5 + 3.0625 = 9.5625 3.0625 + 3.5x + x2 = 9.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x + 1.75) equal to 3.092329219 and -3.092329219.Subproblem 1
x + 1.75 = 3.092329219 Simplifying x + 1.75 = 3.092329219 Reorder the terms: 1.75 + x = 3.092329219 Solving 1.75 + x = 3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.092329219 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.092329219 + -1.75 x = 3.092329219 + -1.75 Combine like terms: 3.092329219 + -1.75 = 1.342329219 x = 1.342329219 Simplifying x = 1.342329219Subproblem 2
x + 1.75 = -3.092329219 Simplifying x + 1.75 = -3.092329219 Reorder the terms: 1.75 + x = -3.092329219 Solving 1.75 + x = -3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.092329219 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.092329219 + -1.75 x = -3.092329219 + -1.75 Combine like terms: -3.092329219 + -1.75 = -4.842329219 x = -4.842329219 Simplifying x = -4.842329219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.342329219, -4.842329219}Solution
x = {1.342329219, -4.842329219}
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