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Simplifying 7x2 + -4x + -35 = 0 Reorder the terms: -35 + -4x + 7x2 = 0 Solving -35 + -4x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.5714285714x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.5714285714x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.5714285714x + x2 = 0 + 5 -0.5714285714x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.5714285714x + x2 = 5 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 5 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 5 + 0.08163265305 Combine like terms: 5 + 0.08163265305 = 5.08163265305 0.08163265305 + -0.5714285714x + x2 = 5.08163265305 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 5.08163265305 Calculate the square root of the right side: 2.254247691 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 2.254247691 and -2.254247691.Subproblem 1
x + -0.2857142857 = 2.254247691 Simplifying x + -0.2857142857 = 2.254247691 Reorder the terms: -0.2857142857 + x = 2.254247691 Solving -0.2857142857 + x = 2.254247691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 2.254247691 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 2.254247691 + 0.2857142857 x = 2.254247691 + 0.2857142857 Combine like terms: 2.254247691 + 0.2857142857 = 2.5399619767 x = 2.5399619767 Simplifying x = 2.5399619767Subproblem 2
x + -0.2857142857 = -2.254247691 Simplifying x + -0.2857142857 = -2.254247691 Reorder the terms: -0.2857142857 + x = -2.254247691 Solving -0.2857142857 + x = -2.254247691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -2.254247691 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -2.254247691 + 0.2857142857 x = -2.254247691 + 0.2857142857 Combine like terms: -2.254247691 + 0.2857142857 = -1.9685334053 x = -1.9685334053 Simplifying x = -1.9685334053Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5399619767, -1.9685334053}
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