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Simplifying 5x2 + -16x + 7 = -2 Reorder the terms: 7 + -16x + 5x2 = -2 Solving 7 + -16x + 5x2 = -2 Solving for variable 'x'. Reorder the terms: 7 + 2 + -16x + 5x2 = -2 + 2 Combine like terms: 7 + 2 = 9 9 + -16x + 5x2 = -2 + 2 Combine like terms: -2 + 2 = 0 9 + -16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + -3.2x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -3.2x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -3.2x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -3.2x + x2 = 0 + -1.8 -3.2x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -3.2x + x2 = -1.8 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 = -1.8 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = -1.8 + 2.56 Combine like terms: -1.8 + 2.56 = 0.76 2.56 + -3.2x + x2 = 0.76 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (x + -1.6) equal to 0.871779789 and -0.871779789.Subproblem 1
x + -1.6 = 0.871779789 Simplifying x + -1.6 = 0.871779789 Reorder the terms: -1.6 + x = 0.871779789 Solving -1.6 + x = 0.871779789 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 = 0.871779789 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 0.871779789 + 1.6 x = 0.871779789 + 1.6 Combine like terms: 0.871779789 + 1.6 = 2.471779789 x = 2.471779789 Simplifying x = 2.471779789Subproblem 2
x + -1.6 = -0.871779789 Simplifying x + -1.6 = -0.871779789 Reorder the terms: -1.6 + x = -0.871779789 Solving -1.6 + x = -0.871779789 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 = -0.871779789 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -0.871779789 + 1.6 x = -0.871779789 + 1.6 Combine like terms: -0.871779789 + 1.6 = 0.728220211 x = 0.728220211 Simplifying x = 0.728220211Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.471779789, 0.728220211}
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