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Simplifying 5x2 + -29x + -63 = 0 Reorder the terms: -63 + -29x + 5x2 = 0 Solving -63 + -29x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.6 + -5.8x + x2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + -5.8x + 12.6 + x2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + -5.8x + x2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + -5.8x + x2 = 0 + 12.6 -5.8x + x2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 -5.8x + x2 = 12.6 The x term is -5.8x. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8x + 8.41 + x2 = 12.6 + 8.41 Reorder the terms: 8.41 + -5.8x + x2 = 12.6 + 8.41 Combine like terms: 12.6 + 8.41 = 21.01 8.41 + -5.8x + x2 = 21.01 Factor a perfect square on the left side: (x + -2.9)(x + -2.9) = 21.01 Calculate the square root of the right side: 4.583666655 Break this problem into two subproblems by setting (x + -2.9) equal to 4.583666655 and -4.583666655.Subproblem 1
x + -2.9 = 4.583666655 Simplifying x + -2.9 = 4.583666655 Reorder the terms: -2.9 + x = 4.583666655 Solving -2.9 + x = 4.583666655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = 4.583666655 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = 4.583666655 + 2.9 x = 4.583666655 + 2.9 Combine like terms: 4.583666655 + 2.9 = 7.483666655 x = 7.483666655 Simplifying x = 7.483666655Subproblem 2
x + -2.9 = -4.583666655 Simplifying x + -2.9 = -4.583666655 Reorder the terms: -2.9 + x = -4.583666655 Solving -2.9 + x = -4.583666655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = -4.583666655 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = -4.583666655 + 2.9 x = -4.583666655 + 2.9 Combine like terms: -4.583666655 + 2.9 = -1.683666655 x = -1.683666655 Simplifying x = -1.683666655Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.483666655, -1.683666655}
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