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Simplifying -5x2 + -18x + 79 = 0 Reorder the terms: 79 + -18x + -5x2 = 0 Solving 79 + -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'. -15.8 + 3.6x + x2 = 0 Move the constant term to the right: Add '15.8' to each side of the equation. -15.8 + 3.6x + 15.8 + x2 = 0 + 15.8 Reorder the terms: -15.8 + 15.8 + 3.6x + x2 = 0 + 15.8 Combine like terms: -15.8 + 15.8 = 0.0 0.0 + 3.6x + x2 = 0 + 15.8 3.6x + x2 = 0 + 15.8 Combine like terms: 0 + 15.8 = 15.8 3.6x + x2 = 15.8 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 = 15.8 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 15.8 + 3.24 Combine like terms: 15.8 + 3.24 = 19.04 3.24 + 3.6x + x2 = 19.04 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 19.04 Calculate the square root of the right side: 4.363484846 Break this problem into two subproblems by setting (x + 1.8) equal to 4.363484846 and -4.363484846.Subproblem 1
x + 1.8 = 4.363484846 Simplifying x + 1.8 = 4.363484846 Reorder the terms: 1.8 + x = 4.363484846 Solving 1.8 + x = 4.363484846 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 = 4.363484846 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 4.363484846 + -1.8 x = 4.363484846 + -1.8 Combine like terms: 4.363484846 + -1.8 = 2.563484846 x = 2.563484846 Simplifying x = 2.563484846Subproblem 2
x + 1.8 = -4.363484846 Simplifying x + 1.8 = -4.363484846 Reorder the terms: 1.8 + x = -4.363484846 Solving 1.8 + x = -4.363484846 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 = -4.363484846 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -4.363484846 + -1.8 x = -4.363484846 + -1.8 Combine like terms: -4.363484846 + -1.8 = -6.163484846 x = -6.163484846 Simplifying x = -6.163484846Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.563484846, -6.163484846}
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