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Simplifying 7x2 + 12x + -34 = 0 Reorder the terms: -34 + 12x + 7x2 = 0 Solving -34 + 12x + 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'. -4.857142857 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '4.857142857' to each side of the equation. -4.857142857 + 1.714285714x + 4.857142857 + x2 = 0 + 4.857142857 Reorder the terms: -4.857142857 + 4.857142857 + 1.714285714x + x2 = 0 + 4.857142857 Combine like terms: -4.857142857 + 4.857142857 = 0.000000000 0.000000000 + 1.714285714x + x2 = 0 + 4.857142857 1.714285714x + x2 = 0 + 4.857142857 Combine like terms: 0 + 4.857142857 = 4.857142857 1.714285714x + x2 = 4.857142857 The x term is 1.714285714x. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714x + 0.7346938773 + x2 = 4.857142857 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 4.857142857 + 0.7346938773 Combine like terms: 4.857142857 + 0.7346938773 = 5.5918367343 0.7346938773 + 1.714285714x + x2 = 5.5918367343 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 5.5918367343 Calculate the square root of the right side: 2.36470648 Break this problem into two subproblems by setting (x + 0.857142857) equal to 2.36470648 and -2.36470648.Subproblem 1
x + 0.857142857 = 2.36470648 Simplifying x + 0.857142857 = 2.36470648 Reorder the terms: 0.857142857 + x = 2.36470648 Solving 0.857142857 + x = 2.36470648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = 2.36470648 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 2.36470648 + -0.857142857 x = 2.36470648 + -0.857142857 Combine like terms: 2.36470648 + -0.857142857 = 1.507563623 x = 1.507563623 Simplifying x = 1.507563623Subproblem 2
x + 0.857142857 = -2.36470648 Simplifying x + 0.857142857 = -2.36470648 Reorder the terms: 0.857142857 + x = -2.36470648 Solving 0.857142857 + x = -2.36470648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = -2.36470648 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -2.36470648 + -0.857142857 x = -2.36470648 + -0.857142857 Combine like terms: -2.36470648 + -0.857142857 = -3.221849337 x = -3.221849337 Simplifying x = -3.221849337Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.507563623, -3.221849337}
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