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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 = 5.64 3.24 + -3.6x + x2 = 5.64 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 5.64 Calculate the square root of the right side: 2.374868417 Break this problem into two subproblems by setting (x + -1.8) equal to 2.374868417 and -2.374868417.Subproblem 1
x + -1.8 = 2.374868417 Simplifying x + -1.8 = 2.374868417 Reorder the terms: -1.8 + x = 2.374868417 Solving -1.8 + x = 2.374868417 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 = 2.374868417 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 2.374868417 + 1.8 x = 2.374868417 + 1.8 Combine like terms: 2.374868417 + 1.8 = 4.174868417 x = 4.174868417 Simplifying x = 4.174868417Subproblem 2
x + -1.8 = -2.374868417 Simplifying x + -1.8 = -2.374868417 Reorder the terms: -1.8 + x = -2.374868417 Solving -1.8 + x = -2.374868417 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 = -2.374868417 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -2.374868417 + 1.8 x = -2.374868417 + 1.8 Combine like terms: -2.374868417 + 1.8 = -0.574868417 x = -0.574868417 Simplifying x = -0.574868417Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.174868417, -0.574868417}
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