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Simplifying 2x2 + 10x + 12 = 7 Reorder the terms: 12 + 10x + 2x2 = 7 Solving 12 + 10x + 2x2 = 7 Solving for variable 'x'. Reorder the terms: 12 + -7 + 10x + 2x2 = 7 + -7 Combine like terms: 12 + -7 = 5 5 + 10x + 2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 5 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 5x + x2 = 0 + -2.5 5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 5x + x2 = -2.5 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 = -2.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -2.5 + 6.25 Combine like terms: -2.5 + 6.25 = 3.75 6.25 + 5x + x2 = 3.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + 2.5) equal to 1.936491673 and -1.936491673.Subproblem 1
x + 2.5 = 1.936491673 Simplifying x + 2.5 = 1.936491673 Reorder the terms: 2.5 + x = 1.936491673 Solving 2.5 + x = 1.936491673 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 = 1.936491673 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.936491673 + -2.5 x = 1.936491673 + -2.5 Combine like terms: 1.936491673 + -2.5 = -0.563508327 x = -0.563508327 Simplifying x = -0.563508327Subproblem 2
x + 2.5 = -1.936491673 Simplifying x + 2.5 = -1.936491673 Reorder the terms: 2.5 + x = -1.936491673 Solving 2.5 + x = -1.936491673 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 = -1.936491673 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.936491673 + -2.5 x = -1.936491673 + -2.5 Combine like terms: -1.936491673 + -2.5 = -4.436491673 x = -4.436491673 Simplifying x = -4.436491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.563508327, -4.436491673}
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