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Simplifying 4x(x + 3) + 2x = x + -8 Reorder the terms: 4x(3 + x) + 2x = x + -8 (3 * 4x + x * 4x) + 2x = x + -8 (12x + 4x2) + 2x = x + -8 Reorder the terms: 12x + 2x + 4x2 = x + -8 Combine like terms: 12x + 2x = 14x 14x + 4x2 = x + -8 Reorder the terms: 14x + 4x2 = -8 + x Solving 14x + 4x2 = -8 + x Solving for variable 'x'. Reorder the terms: 8 + 14x + -1x + 4x2 = -8 + x + 8 + -1x Combine like terms: 14x + -1x = 13x 8 + 13x + 4x2 = -8 + x + 8 + -1x Reorder the terms: 8 + 13x + 4x2 = -8 + 8 + x + -1x Combine like terms: -8 + 8 = 0 8 + 13x + 4x2 = 0 + x + -1x 8 + 13x + 4x2 = x + -1x Combine like terms: x + -1x = 0 8 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + 3.25x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.25x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.25x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.25x + x2 = 0 + -2 3.25x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.25x + x2 = -2 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = -2 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = -2 + 2.640625 Combine like terms: -2 + 2.640625 = 0.640625 2.640625 + 3.25x + x2 = 0.640625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + 1.625) equal to 0.80039053 and -0.80039053.Subproblem 1
x + 1.625 = 0.80039053 Simplifying x + 1.625 = 0.80039053 Reorder the terms: 1.625 + x = 0.80039053 Solving 1.625 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 0.80039053 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 0.80039053 + -1.625 x = 0.80039053 + -1.625 Combine like terms: 0.80039053 + -1.625 = -0.82460947 x = -0.82460947 Simplifying x = -0.82460947Subproblem 2
x + 1.625 = -0.80039053 Simplifying x + 1.625 = -0.80039053 Reorder the terms: 1.625 + x = -0.80039053 Solving 1.625 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -0.80039053 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -0.80039053 + -1.625 x = -0.80039053 + -1.625 Combine like terms: -0.80039053 + -1.625 = -2.42539053 x = -2.42539053 Simplifying x = -2.42539053Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.82460947, -2.42539053}
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