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Simplifying 9x2 + 7x + -14 = 3x Reorder the terms: -14 + 7x + 9x2 = 3x Solving -14 + 7x + 9x2 = 3x Solving for variable 'x'. Reorder the terms: -14 + 7x + -3x + 9x2 = 3x + -3x Combine like terms: 7x + -3x = 4x -14 + 4x + 9x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -14 + 4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 0.4444444444x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 0.4444444444x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 0.4444444444x + x2 = 0 + 1.555555556 0.4444444444x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 0.4444444444x + x2 = 1.555555556 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 1.555555556 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 1.555555556 + 0.04938271604 Combine like terms: 1.555555556 + 0.04938271604 = 1.60493827204 0.04938271604 + 0.4444444444x + x2 = 1.60493827204 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 1.60493827204 Calculate the square root of the right side: 1.266861584 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 1.266861584 and -1.266861584.Subproblem 1
x + 0.2222222222 = 1.266861584 Simplifying x + 0.2222222222 = 1.266861584 Reorder the terms: 0.2222222222 + x = 1.266861584 Solving 0.2222222222 + x = 1.266861584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 1.266861584 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 1.266861584 + -0.2222222222 x = 1.266861584 + -0.2222222222 Combine like terms: 1.266861584 + -0.2222222222 = 1.0446393618 x = 1.0446393618 Simplifying x = 1.0446393618Subproblem 2
x + 0.2222222222 = -1.266861584 Simplifying x + 0.2222222222 = -1.266861584 Reorder the terms: 0.2222222222 + x = -1.266861584 Solving 0.2222222222 + x = -1.266861584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -1.266861584 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -1.266861584 + -0.2222222222 x = -1.266861584 + -0.2222222222 Combine like terms: -1.266861584 + -0.2222222222 = -1.4890838062 x = -1.4890838062 Simplifying x = -1.4890838062Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0446393618, -1.4890838062}
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