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Simplifying 0 = -5x2 + 18x + -12 Reorder the terms: 0 = -12 + 18x + -5x2 Solving 0 = -12 + 18x + -5x2 Solving for variable 'x'. Combine like terms: 0 + 12 = 12 12 + -18x + 5x2 = -12 + 18x + -5x2 + 12 + -18x + 5x2 Reorder the terms: 12 + -18x + 5x2 = -12 + 12 + 18x + -18x + -5x2 + 5x2 Combine like terms: -12 + 12 = 0 12 + -18x + 5x2 = 0 + 18x + -18x + -5x2 + 5x2 12 + -18x + 5x2 = 18x + -18x + -5x2 + 5x2 Combine like terms: 18x + -18x = 0 12 + -18x + 5x2 = 0 + -5x2 + 5x2 12 + -18x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 12 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -3.6x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -3.6x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -3.6x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -3.6x + x2 = 0 + -2.4 -3.6x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -3.6x + x2 = -2.4 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -2.4 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -2.4 + 3.24 Combine like terms: -2.4 + 3.24 = 0.84 3.24 + -3.6x + x2 = 0.84 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (x + -1.8) equal to 0.916515139 and -0.916515139.Subproblem 1
x + -1.8 = 0.916515139 Simplifying x + -1.8 = 0.916515139 Reorder the terms: -1.8 + x = 0.916515139 Solving -1.8 + x = 0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 0.916515139 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 0.916515139 + 1.8 x = 0.916515139 + 1.8 Combine like terms: 0.916515139 + 1.8 = 2.716515139 x = 2.716515139 Simplifying x = 2.716515139Subproblem 2
x + -1.8 = -0.916515139 Simplifying x + -1.8 = -0.916515139 Reorder the terms: -1.8 + x = -0.916515139 Solving -1.8 + x = -0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -0.916515139 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -0.916515139 + 1.8 x = -0.916515139 + 1.8 Combine like terms: -0.916515139 + 1.8 = 0.883484861 x = 0.883484861 Simplifying x = 0.883484861Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.716515139, 0.883484861}
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