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Simplifying (-14x2 + 2x) + -1(5x2 + 5x + -3) = 0 Reorder the terms: (2x + -14x2) + -1(5x2 + 5x + -3) = 0 Remove parenthesis around (2x + -14x2) 2x + -14x2 + -1(5x2 + 5x + -3) = 0 Reorder the terms: 2x + -14x2 + -1(-3 + 5x + 5x2) = 0 2x + -14x2 + (-3 * -1 + 5x * -1 + 5x2 * -1) = 0 2x + -14x2 + (3 + -5x + -5x2) = 0 Reorder the terms: 3 + 2x + -5x + -14x2 + -5x2 = 0 Combine like terms: 2x + -5x = -3x 3 + -3x + -14x2 + -5x2 = 0 Combine like terms: -14x2 + -5x2 = -19x2 3 + -3x + -19x2 = 0 Solving 3 + -3x + -19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. -0.1578947368 + 0.1578947368x + x2 = 0 Move the constant term to the right: Add '0.1578947368' to each side of the equation. -0.1578947368 + 0.1578947368x + 0.1578947368 + x2 = 0 + 0.1578947368 Reorder the terms: -0.1578947368 + 0.1578947368 + 0.1578947368x + x2 = 0 + 0.1578947368 Combine like terms: -0.1578947368 + 0.1578947368 = 0.0000000000 0.0000000000 + 0.1578947368x + x2 = 0 + 0.1578947368 0.1578947368x + x2 = 0 + 0.1578947368 Combine like terms: 0 + 0.1578947368 = 0.1578947368 0.1578947368x + x2 = 0.1578947368 The x term is 0.1578947368x. Take half its coefficient (0.0789473684). Square it (0.006232686977) and add it to both sides. Add '0.006232686977' to each side of the equation. 0.1578947368x + 0.006232686977 + x2 = 0.1578947368 + 0.006232686977 Reorder the terms: 0.006232686977 + 0.1578947368x + x2 = 0.1578947368 + 0.006232686977 Combine like terms: 0.1578947368 + 0.006232686977 = 0.164127423777 0.006232686977 + 0.1578947368x + x2 = 0.164127423777 Factor a perfect square on the left side: (x + 0.0789473684)(x + 0.0789473684) = 0.164127423777 Calculate the square root of the right side: 0.405126429 Break this problem into two subproblems by setting (x + 0.0789473684) equal to 0.405126429 and -0.405126429.Subproblem 1
x + 0.0789473684 = 0.405126429 Simplifying x + 0.0789473684 = 0.405126429 Reorder the terms: 0.0789473684 + x = 0.405126429 Solving 0.0789473684 + x = 0.405126429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0789473684' to each side of the equation. 0.0789473684 + -0.0789473684 + x = 0.405126429 + -0.0789473684 Combine like terms: 0.0789473684 + -0.0789473684 = 0.0000000000 0.0000000000 + x = 0.405126429 + -0.0789473684 x = 0.405126429 + -0.0789473684 Combine like terms: 0.405126429 + -0.0789473684 = 0.3261790606 x = 0.3261790606 Simplifying x = 0.3261790606Subproblem 2
x + 0.0789473684 = -0.405126429 Simplifying x + 0.0789473684 = -0.405126429 Reorder the terms: 0.0789473684 + x = -0.405126429 Solving 0.0789473684 + x = -0.405126429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0789473684' to each side of the equation. 0.0789473684 + -0.0789473684 + x = -0.405126429 + -0.0789473684 Combine like terms: 0.0789473684 + -0.0789473684 = 0.0000000000 0.0000000000 + x = -0.405126429 + -0.0789473684 x = -0.405126429 + -0.0789473684 Combine like terms: -0.405126429 + -0.0789473684 = -0.4840737974 x = -0.4840737974 Simplifying x = -0.4840737974Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3261790606, -0.4840737974}
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