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Simplifying -12x2 + -30x + 7 = 0 Reorder the terms: 7 + -30x + -12x2 = 0 Solving 7 + -30x + -12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.5833333333 + 2.5x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + 2.5x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + 2.5x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + 2.5x + x2 = 0 + 0.5833333333 2.5x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 2.5x + x2 = 0.5833333333 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 0.5833333333 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.5833333333 + 1.5625 Combine like terms: 0.5833333333 + 1.5625 = 2.1458333333 1.5625 + 2.5x + x2 = 2.1458333333 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2.1458333333 Calculate the square root of the right side: 1.464866319 Break this problem into two subproblems by setting (x + 1.25) equal to 1.464866319 and -1.464866319.Subproblem 1
x + 1.25 = 1.464866319 Simplifying x + 1.25 = 1.464866319 Reorder the terms: 1.25 + x = 1.464866319 Solving 1.25 + x = 1.464866319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.464866319 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.464866319 + -1.25 x = 1.464866319 + -1.25 Combine like terms: 1.464866319 + -1.25 = 0.214866319 x = 0.214866319 Simplifying x = 0.214866319Subproblem 2
x + 1.25 = -1.464866319 Simplifying x + 1.25 = -1.464866319 Reorder the terms: 1.25 + x = -1.464866319 Solving 1.25 + x = -1.464866319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.464866319 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.464866319 + -1.25 x = -1.464866319 + -1.25 Combine like terms: -1.464866319 + -1.25 = -2.714866319 x = -2.714866319 Simplifying x = -2.714866319Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.214866319, -2.714866319}
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