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Simplifying 7x2 + 12x = 5 Reorder the terms: 12x + 7x2 = 5 Solving 12x + 7x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 12x + 7x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 12x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 1.714285714x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 1.714285714x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 1.714285714x + x2 = 0 + 0.7142857143 1.714285714x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 1.714285714x + x2 = 0.7142857143 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 = 0.7142857143 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 0.7142857143 + 0.7346938773 Combine like terms: 0.7142857143 + 0.7346938773 = 1.4489795916 0.7346938773 + 1.714285714x + x2 = 1.4489795916 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 1.4489795916 Calculate the square root of the right side: 1.203735682 Break this problem into two subproblems by setting (x + 0.857142857) equal to 1.203735682 and -1.203735682.Subproblem 1
x + 0.857142857 = 1.203735682 Simplifying x + 0.857142857 = 1.203735682 Reorder the terms: 0.857142857 + x = 1.203735682 Solving 0.857142857 + x = 1.203735682 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 = 1.203735682 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 1.203735682 + -0.857142857 x = 1.203735682 + -0.857142857 Combine like terms: 1.203735682 + -0.857142857 = 0.346592825 x = 0.346592825 Simplifying x = 0.346592825Subproblem 2
x + 0.857142857 = -1.203735682 Simplifying x + 0.857142857 = -1.203735682 Reorder the terms: 0.857142857 + x = -1.203735682 Solving 0.857142857 + x = -1.203735682 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 = -1.203735682 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -1.203735682 + -0.857142857 x = -1.203735682 + -0.857142857 Combine like terms: -1.203735682 + -0.857142857 = -2.060878539 x = -2.060878539 Simplifying x = -2.060878539Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.346592825, -2.060878539}
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