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Simplifying 7x2 + 12x = 29 Reorder the terms: 12x + 7x2 = 29 Solving 12x + 7x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + 12x + 7x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 12x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.142857143 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '4.142857143' to each side of the equation. -4.142857143 + 1.714285714x + 4.142857143 + x2 = 0 + 4.142857143 Reorder the terms: -4.142857143 + 4.142857143 + 1.714285714x + x2 = 0 + 4.142857143 Combine like terms: -4.142857143 + 4.142857143 = 0.000000000 0.000000000 + 1.714285714x + x2 = 0 + 4.142857143 1.714285714x + x2 = 0 + 4.142857143 Combine like terms: 0 + 4.142857143 = 4.142857143 1.714285714x + x2 = 4.142857143 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 = 4.142857143 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 4.142857143 + 0.7346938773 Combine like terms: 4.142857143 + 0.7346938773 = 4.8775510203 0.7346938773 + 1.714285714x + x2 = 4.8775510203 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 4.8775510203 Calculate the square root of the right side: 2.208517833 Break this problem into two subproblems by setting (x + 0.857142857) equal to 2.208517833 and -2.208517833.Subproblem 1
x + 0.857142857 = 2.208517833 Simplifying x + 0.857142857 = 2.208517833 Reorder the terms: 0.857142857 + x = 2.208517833 Solving 0.857142857 + x = 2.208517833 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 = 2.208517833 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 2.208517833 + -0.857142857 x = 2.208517833 + -0.857142857 Combine like terms: 2.208517833 + -0.857142857 = 1.351374976 x = 1.351374976 Simplifying x = 1.351374976Subproblem 2
x + 0.857142857 = -2.208517833 Simplifying x + 0.857142857 = -2.208517833 Reorder the terms: 0.857142857 + x = -2.208517833 Solving 0.857142857 + x = -2.208517833 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 = -2.208517833 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -2.208517833 + -0.857142857 x = -2.208517833 + -0.857142857 Combine like terms: -2.208517833 + -0.857142857 = -3.06566069 x = -3.06566069 Simplifying x = -3.06566069Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.351374976, -3.06566069}
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