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Simplifying 7x2 + 28x + -29 = 0 Reorder the terms: -29 + 28x + 7x2 = 0 Solving -29 + 28x + 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'. -4.142857143 + 4x + x2 = 0 Move the constant term to the right: Add '4.142857143' to each side of the equation. -4.142857143 + 4x + 4.142857143 + x2 = 0 + 4.142857143 Reorder the terms: -4.142857143 + 4.142857143 + 4x + x2 = 0 + 4.142857143 Combine like terms: -4.142857143 + 4.142857143 = 0.000000000 0.000000000 + 4x + x2 = 0 + 4.142857143 4x + x2 = 0 + 4.142857143 Combine like terms: 0 + 4.142857143 = 4.142857143 4x + x2 = 4.142857143 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 4.142857143 + 4 Reorder the terms: 4 + 4x + x2 = 4.142857143 + 4 Combine like terms: 4.142857143 + 4 = 8.142857143 4 + 4x + x2 = 8.142857143 Factor a perfect square on the left side: (x + 2)(x + 2) = 8.142857143 Calculate the square root of the right side: 2.853569194 Break this problem into two subproblems by setting (x + 2) equal to 2.853569194 and -2.853569194.Subproblem 1
x + 2 = 2.853569194 Simplifying x + 2 = 2.853569194 Reorder the terms: 2 + x = 2.853569194 Solving 2 + x = 2.853569194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.853569194 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.853569194 + -2 x = 2.853569194 + -2 Combine like terms: 2.853569194 + -2 = 0.853569194 x = 0.853569194 Simplifying x = 0.853569194Subproblem 2
x + 2 = -2.853569194 Simplifying x + 2 = -2.853569194 Reorder the terms: 2 + x = -2.853569194 Solving 2 + x = -2.853569194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.853569194 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.853569194 + -2 x = -2.853569194 + -2 Combine like terms: -2.853569194 + -2 = -4.853569194 x = -4.853569194 Simplifying x = -4.853569194Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.853569194, -4.853569194}
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