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Simplifying 5x2 + 6x + 2(x * 1) = 125 Reorder the terms for easier multiplication: 5x2 + 6x + 2(1x) = 125 Remove parenthesis around (1x) 5x2 + 6x + 2 * 1x = 125 Multiply 2 * 1 5x2 + 6x + 2x = 125 Reorder the terms: 6x + 2x + 5x2 = 125 Combine like terms: 6x + 2x = 8x 8x + 5x2 = 125 Solving 8x + 5x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + 8x + 5x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -25 + 1.6x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 1.6x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 1.6x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 1.6x + x2 = 0 + 25 1.6x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 1.6x + x2 = 25 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 25 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 25 + 0.64 Combine like terms: 25 + 0.64 = 25.64 0.64 + 1.6x + x2 = 25.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 25.64 Calculate the square root of the right side: 5.06359556 Break this problem into two subproblems by setting (x + 0.8) equal to 5.06359556 and -5.06359556.Subproblem 1
x + 0.8 = 5.06359556 Simplifying x + 0.8 = 5.06359556 Reorder the terms: 0.8 + x = 5.06359556 Solving 0.8 + x = 5.06359556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 5.06359556 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 5.06359556 + -0.8 x = 5.06359556 + -0.8 Combine like terms: 5.06359556 + -0.8 = 4.26359556 x = 4.26359556 Simplifying x = 4.26359556Subproblem 2
x + 0.8 = -5.06359556 Simplifying x + 0.8 = -5.06359556 Reorder the terms: 0.8 + x = -5.06359556 Solving 0.8 + x = -5.06359556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -5.06359556 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -5.06359556 + -0.8 x = -5.06359556 + -0.8 Combine like terms: -5.06359556 + -0.8 = -5.86359556 x = -5.86359556 Simplifying x = -5.86359556Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.26359556, -5.86359556}
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