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Simplifying x2 + 10x + x2 + 3x = -10 + 14 Reorder the terms: 10x + 3x + x2 + x2 = -10 + 14 Combine like terms: 10x + 3x = 13x 13x + x2 + x2 = -10 + 14 Combine like terms: x2 + x2 = 2x2 13x + 2x2 = -10 + 14 Combine like terms: -10 + 14 = 4 13x + 2x2 = 4 Solving 13x + 2x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 13x + 2x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 6.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 6.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 6.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6.5x + x2 = 0 + 2 6.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 6.5x + x2 = 2 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 2 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 2 + 10.5625 Combine like terms: 2 + 10.5625 = 12.5625 10.5625 + 6.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + 3.25) equal to 3.54436172 and -3.54436172.Subproblem 1
x + 3.25 = 3.54436172 Simplifying x + 3.25 = 3.54436172 Reorder the terms: 3.25 + x = 3.54436172 Solving 3.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 3.54436172 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.54436172 + -3.25 x = 3.54436172 + -3.25 Combine like terms: 3.54436172 + -3.25 = 0.29436172 x = 0.29436172 Simplifying x = 0.29436172Subproblem 2
x + 3.25 = -3.54436172 Simplifying x + 3.25 = -3.54436172 Reorder the terms: 3.25 + x = -3.54436172 Solving 3.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -3.54436172 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.54436172 + -3.25 x = -3.54436172 + -3.25 Combine like terms: -3.54436172 + -3.25 = -6.79436172 x = -6.79436172 Simplifying x = -6.79436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.29436172, -6.79436172}
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