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Simplifying 5x2 + -16x + 7 = 0 Reorder the terms: 7 + -16x + 5x2 = 0 Solving 7 + -16x + 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'. 1.4 + -3.2x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -3.2x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -3.2x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -3.2x + x2 = 0 + -1.4 -3.2x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -3.2x + x2 = -1.4 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = -1.4 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = -1.4 + 2.56 Combine like terms: -1.4 + 2.56 = 1.16 2.56 + -3.2x + x2 = 1.16 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 1.16 Calculate the square root of the right side: 1.077032961 Break this problem into two subproblems by setting (x + -1.6) equal to 1.077032961 and -1.077032961.Subproblem 1
x + -1.6 = 1.077032961 Simplifying x + -1.6 = 1.077032961 Reorder the terms: -1.6 + x = 1.077032961 Solving -1.6 + x = 1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 1.077032961 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 1.077032961 + 1.6 x = 1.077032961 + 1.6 Combine like terms: 1.077032961 + 1.6 = 2.677032961 x = 2.677032961 Simplifying x = 2.677032961Subproblem 2
x + -1.6 = -1.077032961 Simplifying x + -1.6 = -1.077032961 Reorder the terms: -1.6 + x = -1.077032961 Solving -1.6 + x = -1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -1.077032961 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -1.077032961 + 1.6 x = -1.077032961 + 1.6 Combine like terms: -1.077032961 + 1.6 = 0.522967039 x = 0.522967039 Simplifying x = 0.522967039Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.677032961, 0.522967039}
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