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Simplifying 5x2 + -3x = 135 Reorder the terms: -3x + 5x2 = 135 Solving -3x + 5x2 = 135 Solving for variable 'x'. Reorder the terms: -135 + -3x + 5x2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -27 + -0.6x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -0.6x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -0.6x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -0.6x + x2 = 0 + 27 -0.6x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -0.6x + x2 = 27 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 27 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 27 + 0.09 Combine like terms: 27 + 0.09 = 27.09 0.09 + -0.6x + x2 = 27.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 27.09 Calculate the square root of the right side: 5.204805472 Break this problem into two subproblems by setting (x + -0.3) equal to 5.204805472 and -5.204805472.Subproblem 1
x + -0.3 = 5.204805472 Simplifying x + -0.3 = 5.204805472 Reorder the terms: -0.3 + x = 5.204805472 Solving -0.3 + x = 5.204805472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 5.204805472 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 5.204805472 + 0.3 x = 5.204805472 + 0.3 Combine like terms: 5.204805472 + 0.3 = 5.504805472 x = 5.504805472 Simplifying x = 5.504805472Subproblem 2
x + -0.3 = -5.204805472 Simplifying x + -0.3 = -5.204805472 Reorder the terms: -0.3 + x = -5.204805472 Solving -0.3 + x = -5.204805472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -5.204805472 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -5.204805472 + 0.3 x = -5.204805472 + 0.3 Combine like terms: -5.204805472 + 0.3 = -4.904805472 x = -4.904805472 Simplifying x = -4.904805472Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.504805472, -4.904805472}
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