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Simplifying -5(3 + -2x)(x) = -3x2 + 2 Reorder the terms for easier multiplication: -5x(3 + -2x) = -3x2 + 2 (3 * -5x + -2x * -5x) = -3x2 + 2 (-15x + 10x2) = -3x2 + 2 Reorder the terms: -15x + 10x2 = 2 + -3x2 Solving -15x + 10x2 = 2 + -3x2 Solving for variable 'x'. Reorder the terms: -2 + -15x + 10x2 + 3x2 = 2 + -3x2 + -2 + 3x2 Combine like terms: 10x2 + 3x2 = 13x2 -2 + -15x + 13x2 = 2 + -3x2 + -2 + 3x2 Reorder the terms: -2 + -15x + 13x2 = 2 + -2 + -3x2 + 3x2 Combine like terms: 2 + -2 = 0 -2 + -15x + 13x2 = 0 + -3x2 + 3x2 -2 + -15x + 13x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -2 + -15x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.1538461538 + -1.153846154x + x2 = 0 Move the constant term to the right: Add '0.1538461538' to each side of the equation. -0.1538461538 + -1.153846154x + 0.1538461538 + x2 = 0 + 0.1538461538 Reorder the terms: -0.1538461538 + 0.1538461538 + -1.153846154x + x2 = 0 + 0.1538461538 Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000 0.0000000000 + -1.153846154x + x2 = 0 + 0.1538461538 -1.153846154x + x2 = 0 + 0.1538461538 Combine like terms: 0 + 0.1538461538 = 0.1538461538 -1.153846154x + x2 = 0.1538461538 The x term is -1.153846154x. Take half its coefficient (-0.576923077). Square it (0.3328402368) and add it to both sides. Add '0.3328402368' to each side of the equation. -1.153846154x + 0.3328402368 + x2 = 0.1538461538 + 0.3328402368 Reorder the terms: 0.3328402368 + -1.153846154x + x2 = 0.1538461538 + 0.3328402368 Combine like terms: 0.1538461538 + 0.3328402368 = 0.4866863906 0.3328402368 + -1.153846154x + x2 = 0.4866863906 Factor a perfect square on the left side: (x + -0.576923077)(x + -0.576923077) = 0.4866863906 Calculate the square root of the right side: 0.697629121 Break this problem into two subproblems by setting (x + -0.576923077) equal to 0.697629121 and -0.697629121.Subproblem 1
x + -0.576923077 = 0.697629121 Simplifying x + -0.576923077 = 0.697629121 Reorder the terms: -0.576923077 + x = 0.697629121 Solving -0.576923077 + x = 0.697629121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.576923077' to each side of the equation. -0.576923077 + 0.576923077 + x = 0.697629121 + 0.576923077 Combine like terms: -0.576923077 + 0.576923077 = 0.000000000 0.000000000 + x = 0.697629121 + 0.576923077 x = 0.697629121 + 0.576923077 Combine like terms: 0.697629121 + 0.576923077 = 1.274552198 x = 1.274552198 Simplifying x = 1.274552198Subproblem 2
x + -0.576923077 = -0.697629121 Simplifying x + -0.576923077 = -0.697629121 Reorder the terms: -0.576923077 + x = -0.697629121 Solving -0.576923077 + x = -0.697629121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.576923077' to each side of the equation. -0.576923077 + 0.576923077 + x = -0.697629121 + 0.576923077 Combine like terms: -0.576923077 + 0.576923077 = 0.000000000 0.000000000 + x = -0.697629121 + 0.576923077 x = -0.697629121 + 0.576923077 Combine like terms: -0.697629121 + 0.576923077 = -0.120706044 x = -0.120706044 Simplifying x = -0.120706044Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.274552198, -0.120706044}
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