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Simplifying 5x2 + 1x + -36 = 0 Reorder the terms: -36 + 1x + 5x2 = 0 Solving -36 + 1x + 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'. -7.2 + 0.2x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 0.2x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 0.2x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 0.2x + x2 = 0 + 7.2 0.2x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 0.2x + x2 = 7.2 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 7.2 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 7.2 + 0.01 Combine like terms: 7.2 + 0.01 = 7.21 0.01 + 0.2x + x2 = 7.21 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 7.21 Calculate the square root of the right side: 2.685144316 Break this problem into two subproblems by setting (x + 0.1) equal to 2.685144316 and -2.685144316.Subproblem 1
x + 0.1 = 2.685144316 Simplifying x + 0.1 = 2.685144316 Reorder the terms: 0.1 + x = 2.685144316 Solving 0.1 + x = 2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 2.685144316 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 2.685144316 + -0.1 x = 2.685144316 + -0.1 Combine like terms: 2.685144316 + -0.1 = 2.585144316 x = 2.585144316 Simplifying x = 2.585144316Subproblem 2
x + 0.1 = -2.685144316 Simplifying x + 0.1 = -2.685144316 Reorder the terms: 0.1 + x = -2.685144316 Solving 0.1 + x = -2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -2.685144316 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -2.685144316 + -0.1 x = -2.685144316 + -0.1 Combine like terms: -2.685144316 + -0.1 = -2.785144316 x = -2.785144316 Simplifying x = -2.785144316Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.585144316, -2.785144316}
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