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Simplifying 16x + -4.91(x2) = 7 Solving 16x + -4.91x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 16x + -4.91x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 16x + -4.91x2 = 0 Begin completing the square. Divide all terms by -4.91 the coefficient of the squared term: Divide each side by '-4.91'. 1.425661914 + -3.258655804x + x2 = 0 Move the constant term to the right: Add '-1.425661914' to each side of the equation. 1.425661914 + -3.258655804x + -1.425661914 + x2 = 0 + -1.425661914 Reorder the terms: 1.425661914 + -1.425661914 + -3.258655804x + x2 = 0 + -1.425661914 Combine like terms: 1.425661914 + -1.425661914 = 0.000000000 0.000000000 + -3.258655804x + x2 = 0 + -1.425661914 -3.258655804x + x2 = 0 + -1.425661914 Combine like terms: 0 + -1.425661914 = -1.425661914 -3.258655804x + x2 = -1.425661914 The x term is -3.258655804x. Take half its coefficient (-1.629327902). Square it (2.654709412) and add it to both sides. Add '2.654709412' to each side of the equation. -3.258655804x + 2.654709412 + x2 = -1.425661914 + 2.654709412 Reorder the terms: 2.654709412 + -3.258655804x + x2 = -1.425661914 + 2.654709412 Combine like terms: -1.425661914 + 2.654709412 = 1.229047498 2.654709412 + -3.258655804x + x2 = 1.229047498 Factor a perfect square on the left side: (x + -1.629327902)(x + -1.629327902) = 1.229047498 Calculate the square root of the right side: 1.108624146 Break this problem into two subproblems by setting (x + -1.629327902) equal to 1.108624146 and -1.108624146.Subproblem 1
x + -1.629327902 = 1.108624146 Simplifying x + -1.629327902 = 1.108624146 Reorder the terms: -1.629327902 + x = 1.108624146 Solving -1.629327902 + x = 1.108624146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.629327902' to each side of the equation. -1.629327902 + 1.629327902 + x = 1.108624146 + 1.629327902 Combine like terms: -1.629327902 + 1.629327902 = 0.000000000 0.000000000 + x = 1.108624146 + 1.629327902 x = 1.108624146 + 1.629327902 Combine like terms: 1.108624146 + 1.629327902 = 2.737952048 x = 2.737952048 Simplifying x = 2.737952048Subproblem 2
x + -1.629327902 = -1.108624146 Simplifying x + -1.629327902 = -1.108624146 Reorder the terms: -1.629327902 + x = -1.108624146 Solving -1.629327902 + x = -1.108624146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.629327902' to each side of the equation. -1.629327902 + 1.629327902 + x = -1.108624146 + 1.629327902 Combine like terms: -1.629327902 + 1.629327902 = 0.000000000 0.000000000 + x = -1.108624146 + 1.629327902 x = -1.108624146 + 1.629327902 Combine like terms: -1.108624146 + 1.629327902 = 0.520703756 x = 0.520703756 Simplifying x = 0.520703756Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.737952048, 0.520703756}
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