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Simplifying 5x2 + -32x + 15 = 0 Reorder the terms: 15 + -32x + 5x2 = 0 Solving 15 + -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'. 3 + -6.4x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6.4x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -6.4x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6.4x + x2 = 0 + -3 -6.4x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6.4x + x2 = -3 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 = -3 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = -3 + 10.24 Combine like terms: -3 + 10.24 = 7.24 10.24 + -6.4x + x2 = 7.24 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 7.24 Calculate the square root of the right side: 2.690724809 Break this problem into two subproblems by setting (x + -3.2) equal to 2.690724809 and -2.690724809.Subproblem 1
x + -3.2 = 2.690724809 Simplifying x + -3.2 = 2.690724809 Reorder the terms: -3.2 + x = 2.690724809 Solving -3.2 + x = 2.690724809 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 = 2.690724809 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 2.690724809 + 3.2 x = 2.690724809 + 3.2 Combine like terms: 2.690724809 + 3.2 = 5.890724809 x = 5.890724809 Simplifying x = 5.890724809Subproblem 2
x + -3.2 = -2.690724809 Simplifying x + -3.2 = -2.690724809 Reorder the terms: -3.2 + x = -2.690724809 Solving -3.2 + x = -2.690724809 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 = -2.690724809 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -2.690724809 + 3.2 x = -2.690724809 + 3.2 Combine like terms: -2.690724809 + 3.2 = 0.509275191 x = 0.509275191 Simplifying x = 0.509275191Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.890724809, 0.509275191}
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