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Simplifying 35x + 147(3x2 + 4x) = 3586 Reorder the terms: 35x + 147(4x + 3x2) = 3586 35x + (4x * 147 + 3x2 * 147) = 3586 35x + (588x + 441x2) = 3586 Combine like terms: 35x + 588x = 623x 623x + 441x2 = 3586 Solving 623x + 441x2 = 3586 Solving for variable 'x'. Reorder the terms: -3586 + 623x + 441x2 = 3586 + -3586 Combine like terms: 3586 + -3586 = 0 -3586 + 623x + 441x2 = 0 Begin completing the square. Divide all terms by 441 the coefficient of the squared term: Divide each side by '441'. -8.131519274 + 1.412698413x + x2 = 0 Move the constant term to the right: Add '8.131519274' to each side of the equation. -8.131519274 + 1.412698413x + 8.131519274 + x2 = 0 + 8.131519274 Reorder the terms: -8.131519274 + 8.131519274 + 1.412698413x + x2 = 0 + 8.131519274 Combine like terms: -8.131519274 + 8.131519274 = 0.000000000 0.000000000 + 1.412698413x + x2 = 0 + 8.131519274 1.412698413x + x2 = 0 + 8.131519274 Combine like terms: 0 + 8.131519274 = 8.131519274 1.412698413x + x2 = 8.131519274 The x term is 1.412698413x. Take half its coefficient (0.7063492065). Square it (0.4989292015) and add it to both sides. Add '0.4989292015' to each side of the equation. 1.412698413x + 0.4989292015 + x2 = 8.131519274 + 0.4989292015 Reorder the terms: 0.4989292015 + 1.412698413x + x2 = 8.131519274 + 0.4989292015 Combine like terms: 8.131519274 + 0.4989292015 = 8.6304484755 0.4989292015 + 1.412698413x + x2 = 8.6304484755 Factor a perfect square on the left side: (x + 0.7063492065)(x + 0.7063492065) = 8.6304484755 Calculate the square root of the right side: 2.937762495 Break this problem into two subproblems by setting (x + 0.7063492065) equal to 2.937762495 and -2.937762495.Subproblem 1
x + 0.7063492065 = 2.937762495 Simplifying x + 0.7063492065 = 2.937762495 Reorder the terms: 0.7063492065 + x = 2.937762495 Solving 0.7063492065 + x = 2.937762495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7063492065' to each side of the equation. 0.7063492065 + -0.7063492065 + x = 2.937762495 + -0.7063492065 Combine like terms: 0.7063492065 + -0.7063492065 = 0.0000000000 0.0000000000 + x = 2.937762495 + -0.7063492065 x = 2.937762495 + -0.7063492065 Combine like terms: 2.937762495 + -0.7063492065 = 2.2314132885 x = 2.2314132885 Simplifying x = 2.2314132885Subproblem 2
x + 0.7063492065 = -2.937762495 Simplifying x + 0.7063492065 = -2.937762495 Reorder the terms: 0.7063492065 + x = -2.937762495 Solving 0.7063492065 + x = -2.937762495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7063492065' to each side of the equation. 0.7063492065 + -0.7063492065 + x = -2.937762495 + -0.7063492065 Combine like terms: 0.7063492065 + -0.7063492065 = 0.0000000000 0.0000000000 + x = -2.937762495 + -0.7063492065 x = -2.937762495 + -0.7063492065 Combine like terms: -2.937762495 + -0.7063492065 = -3.6441117015 x = -3.6441117015 Simplifying x = -3.6441117015Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2314132885, -3.6441117015}
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