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Simplifying 2x2 + -5 + -1(x + 7)(3) = 3 Reorder the terms: 2x2 + -5 + -1(7 + x)(3) = 3 Reorder the terms for easier multiplication: 2x2 + -5 + -1 * 3(7 + x) = 3 Multiply -1 * 3 2x2 + -5 + -3(7 + x) = 3 2x2 + -5 + (7 * -3 + x * -3) = 3 2x2 + -5 + (-21 + -3x) = 3 Reorder the terms: -5 + -21 + -3x + 2x2 = 3 Combine like terms: -5 + -21 = -26 -26 + -3x + 2x2 = 3 Solving -26 + -3x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -26 + -3 + -3x + 2x2 = 3 + -3 Combine like terms: -26 + -3 = -29 -29 + -3x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -29 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + -1.5x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + -1.5x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + -1.5x + x2 = 0 + 14.5 -1.5x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 -1.5x + x2 = 14.5 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 = 14.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 14.5 + 0.5625 Combine like terms: 14.5 + 0.5625 = 15.0625 0.5625 + -1.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + -0.75) equal to 3.881043674 and -3.881043674.Subproblem 1
x + -0.75 = 3.881043674 Simplifying x + -0.75 = 3.881043674 Reorder the terms: -0.75 + x = 3.881043674 Solving -0.75 + x = 3.881043674 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 = 3.881043674 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.881043674 + 0.75 x = 3.881043674 + 0.75 Combine like terms: 3.881043674 + 0.75 = 4.631043674 x = 4.631043674 Simplifying x = 4.631043674Subproblem 2
x + -0.75 = -3.881043674 Simplifying x + -0.75 = -3.881043674 Reorder the terms: -0.75 + x = -3.881043674 Solving -0.75 + x = -3.881043674 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 = -3.881043674 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.881043674 + 0.75 x = -3.881043674 + 0.75 Combine like terms: -3.881043674 + 0.75 = -3.131043674 x = -3.131043674 Simplifying x = -3.131043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.631043674, -3.131043674}
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