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Simplifying 5x2 + 18x + -12 = 0 Reorder the terms: -12 + 18x + 5x2 = 0 Solving -12 + 18x + 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 + 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 = 0.574868417 x = 0.574868417 Simplifying x = 0.574868417Subproblem 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 = -4.174868417 x = -4.174868417 Simplifying x = -4.174868417Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.574868417, -4.174868417}
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