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Simplifying 2x2 + 8x + 15 = 224 Reorder the terms: 15 + 8x + 2x2 = 224 Solving 15 + 8x + 2x2 = 224 Solving for variable 'x'. Reorder the terms: 15 + -224 + 8x + 2x2 = 224 + -224 Combine like terms: 15 + -224 = -209 -209 + 8x + 2x2 = 224 + -224 Combine like terms: 224 + -224 = 0 -209 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -104.5 + 4x + x2 = 0 Move the constant term to the right: Add '104.5' to each side of the equation. -104.5 + 4x + 104.5 + x2 = 0 + 104.5 Reorder the terms: -104.5 + 104.5 + 4x + x2 = 0 + 104.5 Combine like terms: -104.5 + 104.5 = 0.0 0.0 + 4x + x2 = 0 + 104.5 4x + x2 = 0 + 104.5 Combine like terms: 0 + 104.5 = 104.5 4x + x2 = 104.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 104.5 + 4 Reorder the terms: 4 + 4x + x2 = 104.5 + 4 Combine like terms: 104.5 + 4 = 108.5 4 + 4x + x2 = 108.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 108.5 Calculate the square root of the right side: 10.416333328 Break this problem into two subproblems by setting (x + 2) equal to 10.416333328 and -10.416333328.Subproblem 1
x + 2 = 10.416333328 Simplifying x + 2 = 10.416333328 Reorder the terms: 2 + x = 10.416333328 Solving 2 + x = 10.416333328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 10.416333328 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.416333328 + -2 x = 10.416333328 + -2 Combine like terms: 10.416333328 + -2 = 8.416333328 x = 8.416333328 Simplifying x = 8.416333328Subproblem 2
x + 2 = -10.416333328 Simplifying x + 2 = -10.416333328 Reorder the terms: 2 + x = -10.416333328 Solving 2 + x = -10.416333328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -10.416333328 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.416333328 + -2 x = -10.416333328 + -2 Combine like terms: -10.416333328 + -2 = -12.416333328 x = -12.416333328 Simplifying x = -12.416333328Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.416333328, -12.416333328}
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