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Simplifying x2 + 5x + 12 = 70 Reorder the terms: 12 + 5x + x2 = 70 Solving 12 + 5x + x2 = 70 Solving for variable 'x'. Reorder the terms: 12 + -70 + 5x + x2 = 70 + -70 Combine like terms: 12 + -70 = -58 -58 + 5x + x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -58 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + 5x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 5x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 5x + x2 = 0 + 58 5x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 5x + x2 = 58 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 58 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 58 + 6.25 Combine like terms: 58 + 6.25 = 64.25 6.25 + 5x + x2 = 64.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + 2.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + 2.5 = 8.015609771 Simplifying x + 2.5 = 8.015609771 Reorder the terms: 2.5 + x = 8.015609771 Solving 2.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 8.015609771 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 8.015609771 + -2.5 x = 8.015609771 + -2.5 Combine like terms: 8.015609771 + -2.5 = 5.515609771 x = 5.515609771 Simplifying x = 5.515609771Subproblem 2
x + 2.5 = -8.015609771 Simplifying x + 2.5 = -8.015609771 Reorder the terms: 2.5 + x = -8.015609771 Solving 2.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -8.015609771 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -8.015609771 + -2.5 x = -8.015609771 + -2.5 Combine like terms: -8.015609771 + -2.5 = -10.515609771 x = -10.515609771 Simplifying x = -10.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.515609771, -10.515609771}
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