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Simplifying 7x2 + -7 = 12x + 36 Reorder the terms: -7 + 7x2 = 12x + 36 Reorder the terms: -7 + 7x2 = 36 + 12x Solving -7 + 7x2 = 36 + 12x Solving for variable 'x'. Reorder the terms: -7 + -36 + -12x + 7x2 = 36 + 12x + -36 + -12x Combine like terms: -7 + -36 = -43 -43 + -12x + 7x2 = 36 + 12x + -36 + -12x Reorder the terms: -43 + -12x + 7x2 = 36 + -36 + 12x + -12x Combine like terms: 36 + -36 = 0 -43 + -12x + 7x2 = 0 + 12x + -12x -43 + -12x + 7x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -43 + -12x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -6.142857143 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '6.142857143' to each side of the equation. -6.142857143 + -1.714285714x + 6.142857143 + x2 = 0 + 6.142857143 Reorder the terms: -6.142857143 + 6.142857143 + -1.714285714x + x2 = 0 + 6.142857143 Combine like terms: -6.142857143 + 6.142857143 = 0.000000000 0.000000000 + -1.714285714x + x2 = 0 + 6.142857143 -1.714285714x + x2 = 0 + 6.142857143 Combine like terms: 0 + 6.142857143 = 6.142857143 -1.714285714x + x2 = 6.142857143 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 = 6.142857143 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = 6.142857143 + 0.7346938773 Combine like terms: 6.142857143 + 0.7346938773 = 6.8775510203 0.7346938773 + -1.714285714x + x2 = 6.8775510203 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 6.8775510203 Calculate the square root of the right side: 2.622508536 Break this problem into two subproblems by setting (x + -0.857142857) equal to 2.622508536 and -2.622508536.Subproblem 1
x + -0.857142857 = 2.622508536 Simplifying x + -0.857142857 = 2.622508536 Reorder the terms: -0.857142857 + x = 2.622508536 Solving -0.857142857 + x = 2.622508536 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 = 2.622508536 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 2.622508536 + 0.857142857 x = 2.622508536 + 0.857142857 Combine like terms: 2.622508536 + 0.857142857 = 3.479651393 x = 3.479651393 Simplifying x = 3.479651393Subproblem 2
x + -0.857142857 = -2.622508536 Simplifying x + -0.857142857 = -2.622508536 Reorder the terms: -0.857142857 + x = -2.622508536 Solving -0.857142857 + x = -2.622508536 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 = -2.622508536 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -2.622508536 + 0.857142857 x = -2.622508536 + 0.857142857 Combine like terms: -2.622508536 + 0.857142857 = -1.765365679 x = -1.765365679 Simplifying x = -1.765365679Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.479651393, -1.765365679}
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