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Simplifying -5x2 + 9x + 12 = 0 Reorder the terms: 12 + 9x + -5x2 = 0 Solving 12 + 9x + -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'. -2.4 + -1.8x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -1.8x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -1.8x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -1.8x + x2 = 0 + 2.4 -1.8x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -1.8x + x2 = 2.4 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 2.4 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 2.4 + 0.81 Combine like terms: 2.4 + 0.81 = 3.21 0.81 + -1.8x + x2 = 3.21 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 3.21 Calculate the square root of the right side: 1.791647287 Break this problem into two subproblems by setting (x + -0.9) equal to 1.791647287 and -1.791647287.Subproblem 1
x + -0.9 = 1.791647287 Simplifying x + -0.9 = 1.791647287 Reorder the terms: -0.9 + x = 1.791647287 Solving -0.9 + x = 1.791647287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 1.791647287 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 1.791647287 + 0.9 x = 1.791647287 + 0.9 Combine like terms: 1.791647287 + 0.9 = 2.691647287 x = 2.691647287 Simplifying x = 2.691647287Subproblem 2
x + -0.9 = -1.791647287 Simplifying x + -0.9 = -1.791647287 Reorder the terms: -0.9 + x = -1.791647287 Solving -0.9 + x = -1.791647287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -1.791647287 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -1.791647287 + 0.9 x = -1.791647287 + 0.9 Combine like terms: -1.791647287 + 0.9 = -0.891647287 x = -0.891647287 Simplifying x = -0.891647287Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.691647287, -0.891647287}
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