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Simplifying 10 + 3x + 2x(x + -3) = 293 Reorder the terms: 10 + 3x + 2x(-3 + x) = 293 10 + 3x + (-3 * 2x + x * 2x) = 293 10 + 3x + (-6x + 2x2) = 293 Combine like terms: 3x + -6x = -3x 10 + -3x + 2x2 = 293 Solving 10 + -3x + 2x2 = 293 Solving for variable 'x'. Reorder the terms: 10 + -293 + -3x + 2x2 = 293 + -293 Combine like terms: 10 + -293 = -283 -283 + -3x + 2x2 = 293 + -293 Combine like terms: 293 + -293 = 0 -283 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -141.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '141.5' to each side of the equation. -141.5 + -1.5x + 141.5 + x2 = 0 + 141.5 Reorder the terms: -141.5 + 141.5 + -1.5x + x2 = 0 + 141.5 Combine like terms: -141.5 + 141.5 = 0.0 0.0 + -1.5x + x2 = 0 + 141.5 -1.5x + x2 = 0 + 141.5 Combine like terms: 0 + 141.5 = 141.5 -1.5x + x2 = 141.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 141.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 141.5 + 0.5625 Combine like terms: 141.5 + 0.5625 = 142.0625 0.5625 + -1.5x + x2 = 142.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 142.0625 Calculate the square root of the right side: 11.918997441 Break this problem into two subproblems by setting (x + -0.75) equal to 11.918997441 and -11.918997441.Subproblem 1
x + -0.75 = 11.918997441 Simplifying x + -0.75 = 11.918997441 Reorder the terms: -0.75 + x = 11.918997441 Solving -0.75 + x = 11.918997441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 11.918997441 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 11.918997441 + 0.75 x = 11.918997441 + 0.75 Combine like terms: 11.918997441 + 0.75 = 12.668997441 x = 12.668997441 Simplifying x = 12.668997441Subproblem 2
x + -0.75 = -11.918997441 Simplifying x + -0.75 = -11.918997441 Reorder the terms: -0.75 + x = -11.918997441 Solving -0.75 + x = -11.918997441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -11.918997441 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -11.918997441 + 0.75 x = -11.918997441 + 0.75 Combine like terms: -11.918997441 + 0.75 = -11.168997441 x = -11.168997441 Simplifying x = -11.168997441Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.668997441, -11.168997441}
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