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Simplifying 5x2 + 32x + -11 = 0 Reorder the terms: -11 + 32x + 5x2 = 0 Solving -11 + 32x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + 6.4x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 6.4x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 6.4x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 6.4x + x2 = 0 + 2.2 6.4x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 6.4x + x2 = 2.2 The x term is 6.4x. Take half its coefficient (3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. 6.4x + 10.24 + x2 = 2.2 + 10.24 Reorder the terms: 10.24 + 6.4x + x2 = 2.2 + 10.24 Combine like terms: 2.2 + 10.24 = 12.44 10.24 + 6.4x + x2 = 12.44 Factor a perfect square on the left side: (x + 3.2)(x + 3.2) = 12.44 Calculate the square root of the right side: 3.527038418 Break this problem into two subproblems by setting (x + 3.2) equal to 3.527038418 and -3.527038418.Subproblem 1
x + 3.2 = 3.527038418 Simplifying x + 3.2 = 3.527038418 Reorder the terms: 3.2 + x = 3.527038418 Solving 3.2 + x = 3.527038418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 3.527038418 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 3.527038418 + -3.2 x = 3.527038418 + -3.2 Combine like terms: 3.527038418 + -3.2 = 0.327038418 x = 0.327038418 Simplifying x = 0.327038418Subproblem 2
x + 3.2 = -3.527038418 Simplifying x + 3.2 = -3.527038418 Reorder the terms: 3.2 + x = -3.527038418 Solving 3.2 + x = -3.527038418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = -3.527038418 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -3.527038418 + -3.2 x = -3.527038418 + -3.2 Combine like terms: -3.527038418 + -3.2 = -6.727038418 x = -6.727038418 Simplifying x = -6.727038418Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.327038418, -6.727038418}
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