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Simplifying 2x2 + 10x = 9 Reorder the terms: 10x + 2x2 = 9 Solving 10x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 10x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 5x + x2 = 0 + 4.5 5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 5x + x2 = 4.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 4.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 4.5 + 6.25 Combine like terms: 4.5 + 6.25 = 10.75 6.25 + 5x + x2 = 10.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (x + 2.5) equal to 3.278719262 and -3.278719262.Subproblem 1
x + 2.5 = 3.278719262 Simplifying x + 2.5 = 3.278719262 Reorder the terms: 2.5 + x = 3.278719262 Solving 2.5 + x = 3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.278719262 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.278719262 + -2.5 x = 3.278719262 + -2.5 Combine like terms: 3.278719262 + -2.5 = 0.778719262 x = 0.778719262 Simplifying x = 0.778719262Subproblem 2
x + 2.5 = -3.278719262 Simplifying x + 2.5 = -3.278719262 Reorder the terms: 2.5 + x = -3.278719262 Solving 2.5 + x = -3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.278719262 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.278719262 + -2.5 x = -3.278719262 + -2.5 Combine like terms: -3.278719262 + -2.5 = -5.778719262 x = -5.778719262 Simplifying x = -5.778719262Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.778719262, -5.778719262}
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