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Simplifying -7x2 + 14x + 12 = 0 Reorder the terms: 12 + 14x + -7x2 = 0 Solving 12 + 14x + -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'. -1.714285714 + -2x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -2x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -2x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.714285714 -2x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -2x + x2 = 1.714285714 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 = 1.714285714 + 1 Reorder the terms: 1 + -2x + x2 = 1.714285714 + 1 Combine like terms: 1.714285714 + 1 = 2.714285714 1 + -2x + x2 = 2.714285714 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.714285714 Calculate the square root of the right side: 1.647508942 Break this problem into two subproblems by setting (x + -1) equal to 1.647508942 and -1.647508942.Subproblem 1
x + -1 = 1.647508942 Simplifying x + -1 = 1.647508942 Reorder the terms: -1 + x = 1.647508942 Solving -1 + x = 1.647508942 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 = 1.647508942 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.647508942 + 1 x = 1.647508942 + 1 Combine like terms: 1.647508942 + 1 = 2.647508942 x = 2.647508942 Simplifying x = 2.647508942Subproblem 2
x + -1 = -1.647508942 Simplifying x + -1 = -1.647508942 Reorder the terms: -1 + x = -1.647508942 Solving -1 + x = -1.647508942 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 = -1.647508942 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.647508942 + 1 x = -1.647508942 + 1 Combine like terms: -1.647508942 + 1 = -0.647508942 x = -0.647508942 Simplifying x = -0.647508942Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.647508942, -0.647508942}
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