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Simplifying 7x2 + -14x + -78 = -9 Reorder the terms: -78 + -14x + 7x2 = -9 Solving -78 + -14x + 7x2 = -9 Solving for variable 'x'. Reorder the terms: -78 + 9 + -14x + 7x2 = -9 + 9 Combine like terms: -78 + 9 = -69 -69 + -14x + 7x2 = -9 + 9 Combine like terms: -9 + 9 = 0 -69 + -14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -9.857142857 + -2x + x2 = 0 Move the constant term to the right: Add '9.857142857' to each side of the equation. -9.857142857 + -2x + 9.857142857 + x2 = 0 + 9.857142857 Reorder the terms: -9.857142857 + 9.857142857 + -2x + x2 = 0 + 9.857142857 Combine like terms: -9.857142857 + 9.857142857 = 0.000000000 0.000000000 + -2x + x2 = 0 + 9.857142857 -2x + x2 = 0 + 9.857142857 Combine like terms: 0 + 9.857142857 = 9.857142857 -2x + x2 = 9.857142857 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 9.857142857 + 1 Reorder the terms: 1 + -2x + x2 = 9.857142857 + 1 Combine like terms: 9.857142857 + 1 = 10.857142857 1 + -2x + x2 = 10.857142857 Factor a perfect square on the left side: (x + -1)(x + -1) = 10.857142857 Calculate the square root of the right side: 3.295017884 Break this problem into two subproblems by setting (x + -1) equal to 3.295017884 and -3.295017884.Subproblem 1
x + -1 = 3.295017884 Simplifying x + -1 = 3.295017884 Reorder the terms: -1 + x = 3.295017884 Solving -1 + x = 3.295017884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.295017884 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.295017884 + 1 x = 3.295017884 + 1 Combine like terms: 3.295017884 + 1 = 4.295017884 x = 4.295017884 Simplifying x = 4.295017884Subproblem 2
x + -1 = -3.295017884 Simplifying x + -1 = -3.295017884 Reorder the terms: -1 + x = -3.295017884 Solving -1 + x = -3.295017884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.295017884 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.295017884 + 1 x = -3.295017884 + 1 Combine like terms: -3.295017884 + 1 = -2.295017884 x = -2.295017884 Simplifying x = -2.295017884Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.295017884, -2.295017884}
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