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Simplifying x2 + -4(30x2 + -44x + -10) = 0 Reorder the terms: x2 + -4(-10 + -44x + 30x2) = 0 x2 + (-10 * -4 + -44x * -4 + 30x2 * -4) = 0 x2 + (40 + 176x + -120x2) = 0 Reorder the terms: 40 + 176x + x2 + -120x2 = 0 Combine like terms: x2 + -120x2 = -119x2 40 + 176x + -119x2 = 0 Solving 40 + 176x + -119x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -119 the coefficient of the squared term: Divide each side by '-119'. -0.3361344538 + -1.478991597x + x2 = 0 Move the constant term to the right: Add '0.3361344538' to each side of the equation. -0.3361344538 + -1.478991597x + 0.3361344538 + x2 = 0 + 0.3361344538 Reorder the terms: -0.3361344538 + 0.3361344538 + -1.478991597x + x2 = 0 + 0.3361344538 Combine like terms: -0.3361344538 + 0.3361344538 = 0.0000000000 0.0000000000 + -1.478991597x + x2 = 0 + 0.3361344538 -1.478991597x + x2 = 0 + 0.3361344538 Combine like terms: 0 + 0.3361344538 = 0.3361344538 -1.478991597x + x2 = 0.3361344538 The x term is -1.478991597x. Take half its coefficient (-0.7394957985). Square it (0.5468540360) and add it to both sides. Add '0.5468540360' to each side of the equation. -1.478991597x + 0.5468540360 + x2 = 0.3361344538 + 0.5468540360 Reorder the terms: 0.5468540360 + -1.478991597x + x2 = 0.3361344538 + 0.5468540360 Combine like terms: 0.3361344538 + 0.5468540360 = 0.8829884898 0.5468540360 + -1.478991597x + x2 = 0.8829884898 Factor a perfect square on the left side: (x + -0.7394957985)(x + -0.7394957985) = 0.8829884898 Calculate the square root of the right side: 0.939674672 Break this problem into two subproblems by setting (x + -0.7394957985) equal to 0.939674672 and -0.939674672.Subproblem 1
x + -0.7394957985 = 0.939674672 Simplifying x + -0.7394957985 = 0.939674672 Reorder the terms: -0.7394957985 + x = 0.939674672 Solving -0.7394957985 + x = 0.939674672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7394957985' to each side of the equation. -0.7394957985 + 0.7394957985 + x = 0.939674672 + 0.7394957985 Combine like terms: -0.7394957985 + 0.7394957985 = 0.0000000000 0.0000000000 + x = 0.939674672 + 0.7394957985 x = 0.939674672 + 0.7394957985 Combine like terms: 0.939674672 + 0.7394957985 = 1.6791704705 x = 1.6791704705 Simplifying x = 1.6791704705Subproblem 2
x + -0.7394957985 = -0.939674672 Simplifying x + -0.7394957985 = -0.939674672 Reorder the terms: -0.7394957985 + x = -0.939674672 Solving -0.7394957985 + x = -0.939674672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7394957985' to each side of the equation. -0.7394957985 + 0.7394957985 + x = -0.939674672 + 0.7394957985 Combine like terms: -0.7394957985 + 0.7394957985 = 0.0000000000 0.0000000000 + x = -0.939674672 + 0.7394957985 x = -0.939674672 + 0.7394957985 Combine like terms: -0.939674672 + 0.7394957985 = -0.2001788735 x = -0.2001788735 Simplifying x = -0.2001788735Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6791704705, -0.2001788735}
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