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Simplifying 18x + -16x2 = 0.75 Solving 18x + -16x2 = 0.75 Solving for variable 'x'. Reorder the terms: -0.75 + 18x + -16x2 = 0.75 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 -0.75 + 18x + -16x2 = 0.00 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.046875 + -1.125x + x2 = 0.00 Move the constant term to the right: Add '-0.046875' to each side of the equation. 0.046875 + -1.125x + -0.046875 + x2 = 0.00 + -0.046875 Reorder the terms: 0.046875 + -0.046875 + -1.125x + x2 = 0.00 + -0.046875 Combine like terms: 0.046875 + -0.046875 = 0.000000 0.000000 + -1.125x + x2 = 0.00 + -0.046875 -1.125x + x2 = 0.00 + -0.046875 Combine like terms: 0.00 + -0.046875 = -0.046875 -1.125x + x2 = -0.046875 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = -0.046875 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = -0.046875 + 0.31640625 Combine like terms: -0.046875 + 0.31640625 = 0.26953125 0.31640625 + -1.125x + x2 = 0.26953125 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 0.26953125 Calculate the square root of the right side: 0.519163991 Break this problem into two subproblems by setting (x + -0.5625) equal to 0.519163991 and -0.519163991.Subproblem 1
x + -0.5625 = 0.519163991 Simplifying x + -0.5625 = 0.519163991 Reorder the terms: -0.5625 + x = 0.519163991 Solving -0.5625 + x = 0.519163991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 0.519163991 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 0.519163991 + 0.5625 x = 0.519163991 + 0.5625 Combine like terms: 0.519163991 + 0.5625 = 1.081663991 x = 1.081663991 Simplifying x = 1.081663991Subproblem 2
x + -0.5625 = -0.519163991 Simplifying x + -0.5625 = -0.519163991 Reorder the terms: -0.5625 + x = -0.519163991 Solving -0.5625 + x = -0.519163991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -0.519163991 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -0.519163991 + 0.5625 x = -0.519163991 + 0.5625 Combine like terms: -0.519163991 + 0.5625 = 0.043336009 x = 0.043336009 Simplifying x = 0.043336009Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.081663991, 0.043336009}
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