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Simplifying (5x2 + -7x) + -1(3x2 + 2x + 1) = 0 Reorder the terms: (-7x + 5x2) + -1(3x2 + 2x + 1) = 0 Remove parenthesis around (-7x + 5x2) -7x + 5x2 + -1(3x2 + 2x + 1) = 0 Reorder the terms: -7x + 5x2 + -1(1 + 2x + 3x2) = 0 -7x + 5x2 + (1 * -1 + 2x * -1 + 3x2 * -1) = 0 -7x + 5x2 + (-1 + -2x + -3x2) = 0 Reorder the terms: -1 + -7x + -2x + 5x2 + -3x2 = 0 Combine like terms: -7x + -2x = -9x -1 + -9x + 5x2 + -3x2 = 0 Combine like terms: 5x2 + -3x2 = 2x2 -1 + -9x + 2x2 = 0 Solving -1 + -9x + 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'. -0.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -4.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -4.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -4.5x + x2 = 0 + 0.5 -4.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -4.5x + x2 = 0.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 0.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 0.5 + 5.0625 Combine like terms: 0.5 + 5.0625 = 5.5625 5.0625 + -4.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + -2.25) equal to 2.358495283 and -2.358495283.Subproblem 1
x + -2.25 = 2.358495283 Simplifying x + -2.25 = 2.358495283 Reorder the terms: -2.25 + x = 2.358495283 Solving -2.25 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.358495283 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.358495283 + 2.25 x = 2.358495283 + 2.25 Combine like terms: 2.358495283 + 2.25 = 4.608495283 x = 4.608495283 Simplifying x = 4.608495283Subproblem 2
x + -2.25 = -2.358495283 Simplifying x + -2.25 = -2.358495283 Reorder the terms: -2.25 + x = -2.358495283 Solving -2.25 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.358495283 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.358495283 + 2.25 x = -2.358495283 + 2.25 Combine like terms: -2.358495283 + 2.25 = -0.108495283 x = -0.108495283 Simplifying x = -0.108495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.608495283, -0.108495283}
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