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Simplifying 5x2 + -32x + 47 = 0 Reorder the terms: 47 + -32x + 5x2 = 0 Solving 47 + -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'. 9.4 + -6.4x + x2 = 0 Move the constant term to the right: Add '-9.4' to each side of the equation. 9.4 + -6.4x + -9.4 + x2 = 0 + -9.4 Reorder the terms: 9.4 + -9.4 + -6.4x + x2 = 0 + -9.4 Combine like terms: 9.4 + -9.4 = 0.0 0.0 + -6.4x + x2 = 0 + -9.4 -6.4x + x2 = 0 + -9.4 Combine like terms: 0 + -9.4 = -9.4 -6.4x + x2 = -9.4 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 = -9.4 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = -9.4 + 10.24 Combine like terms: -9.4 + 10.24 = 0.84 10.24 + -6.4x + x2 = 0.84 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (x + -3.2) equal to 0.916515139 and -0.916515139.Subproblem 1
x + -3.2 = 0.916515139 Simplifying x + -3.2 = 0.916515139 Reorder the terms: -3.2 + x = 0.916515139 Solving -3.2 + x = 0.916515139 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 = 0.916515139 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 0.916515139 + 3.2 x = 0.916515139 + 3.2 Combine like terms: 0.916515139 + 3.2 = 4.116515139 x = 4.116515139 Simplifying x = 4.116515139Subproblem 2
x + -3.2 = -0.916515139 Simplifying x + -3.2 = -0.916515139 Reorder the terms: -3.2 + x = -0.916515139 Solving -3.2 + x = -0.916515139 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 = -0.916515139 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -0.916515139 + 3.2 x = -0.916515139 + 3.2 Combine like terms: -0.916515139 + 3.2 = 2.283484861 x = 2.283484861 Simplifying x = 2.283484861Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.116515139, 2.283484861}
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