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Simplifying 7x + 5 + -2x2 = 0 Reorder the terms: 5 + 7x + -2x2 = 0 Solving 5 + 7x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.5x + x2 = 0 + 2.5 -3.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.5x + x2 = 2.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 2.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 2.5 + 3.0625 Combine like terms: 2.5 + 3.0625 = 5.5625 3.0625 + -3.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + -1.75) equal to 2.358495283 and -2.358495283.Subproblem 1
x + -1.75 = 2.358495283 Simplifying x + -1.75 = 2.358495283 Reorder the terms: -1.75 + x = 2.358495283 Solving -1.75 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.358495283 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.358495283 + 1.75 x = 2.358495283 + 1.75 Combine like terms: 2.358495283 + 1.75 = 4.108495283 x = 4.108495283 Simplifying x = 4.108495283Subproblem 2
x + -1.75 = -2.358495283 Simplifying x + -1.75 = -2.358495283 Reorder the terms: -1.75 + x = -2.358495283 Solving -1.75 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.358495283 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.358495283 + 1.75 x = -2.358495283 + 1.75 Combine like terms: -2.358495283 + 1.75 = -0.608495283 x = -0.608495283 Simplifying x = -0.608495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.108495283, -0.608495283}
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