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Simplifying 5x2 + -3x = 25 Reorder the terms: -3x + 5x2 = 25 Solving -3x + 5x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -3x + 5x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + -0.6x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.6x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.6x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.6x + x2 = 0 + 5 -0.6x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.6x + x2 = 5 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 = 5 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 5 + 0.09 Combine like terms: 5 + 0.09 = 5.09 0.09 + -0.6x + x2 = 5.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 5.09 Calculate the square root of the right side: 2.256102835 Break this problem into two subproblems by setting (x + -0.3) equal to 2.256102835 and -2.256102835.Subproblem 1
x + -0.3 = 2.256102835 Simplifying x + -0.3 = 2.256102835 Reorder the terms: -0.3 + x = 2.256102835 Solving -0.3 + x = 2.256102835 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 = 2.256102835 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 2.256102835 + 0.3 x = 2.256102835 + 0.3 Combine like terms: 2.256102835 + 0.3 = 2.556102835 x = 2.556102835 Simplifying x = 2.556102835Subproblem 2
x + -0.3 = -2.256102835 Simplifying x + -0.3 = -2.256102835 Reorder the terms: -0.3 + x = -2.256102835 Solving -0.3 + x = -2.256102835 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 = -2.256102835 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -2.256102835 + 0.3 x = -2.256102835 + 0.3 Combine like terms: -2.256102835 + 0.3 = -1.956102835 x = -1.956102835 Simplifying x = -1.956102835Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.556102835, -1.956102835}
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