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Simplifying 5x2 = 3x + 56 Reorder the terms: 5x2 = 56 + 3x Solving 5x2 = 56 + 3x Solving for variable 'x'. Reorder the terms: -56 + -3x + 5x2 = 56 + 3x + -56 + -3x Reorder the terms: -56 + -3x + 5x2 = 56 + -56 + 3x + -3x Combine like terms: 56 + -56 = 0 -56 + -3x + 5x2 = 0 + 3x + -3x -56 + -3x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -56 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11.2 + -0.6x + x2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + -0.6x + 11.2 + x2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + -0.6x + x2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + -0.6x + x2 = 0 + 11.2 -0.6x + x2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 -0.6x + x2 = 11.2 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 = 11.2 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 11.2 + 0.09 Combine like terms: 11.2 + 0.09 = 11.29 0.09 + -0.6x + x2 = 11.29 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 11.29 Calculate the square root of the right side: 3.360059523 Break this problem into two subproblems by setting (x + -0.3) equal to 3.360059523 and -3.360059523.Subproblem 1
x + -0.3 = 3.360059523 Simplifying x + -0.3 = 3.360059523 Reorder the terms: -0.3 + x = 3.360059523 Solving -0.3 + x = 3.360059523 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 = 3.360059523 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 3.360059523 + 0.3 x = 3.360059523 + 0.3 Combine like terms: 3.360059523 + 0.3 = 3.660059523 x = 3.660059523 Simplifying x = 3.660059523Subproblem 2
x + -0.3 = -3.360059523 Simplifying x + -0.3 = -3.360059523 Reorder the terms: -0.3 + x = -3.360059523 Solving -0.3 + x = -3.360059523 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 = -3.360059523 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -3.360059523 + 0.3 x = -3.360059523 + 0.3 Combine like terms: -3.360059523 + 0.3 = -3.060059523 x = -3.060059523 Simplifying x = -3.060059523Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.660059523, -3.060059523}
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