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Simplifying 49x2 + -88x + 16 = 0 Reorder the terms: 16 + -88x + 49x2 = 0 Solving 16 + -88x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.3265306122 + -1.795918367x + x2 = 0 Move the constant term to the right: Add '-0.3265306122' to each side of the equation. 0.3265306122 + -1.795918367x + -0.3265306122 + x2 = 0 + -0.3265306122 Reorder the terms: 0.3265306122 + -0.3265306122 + -1.795918367x + x2 = 0 + -0.3265306122 Combine like terms: 0.3265306122 + -0.3265306122 = 0.0000000000 0.0000000000 + -1.795918367x + x2 = 0 + -0.3265306122 -1.795918367x + x2 = 0 + -0.3265306122 Combine like terms: 0 + -0.3265306122 = -0.3265306122 -1.795918367x + x2 = -0.3265306122 The x term is -1.795918367x. Take half its coefficient (-0.8979591835). Square it (0.8063306952) and add it to both sides. Add '0.8063306952' to each side of the equation. -1.795918367x + 0.8063306952 + x2 = -0.3265306122 + 0.8063306952 Reorder the terms: 0.8063306952 + -1.795918367x + x2 = -0.3265306122 + 0.8063306952 Combine like terms: -0.3265306122 + 0.8063306952 = 0.479800083 0.8063306952 + -1.795918367x + x2 = 0.479800083 Factor a perfect square on the left side: (x + -0.8979591835)(x + -0.8979591835) = 0.479800083 Calculate the square root of the right side: 0.69267603 Break this problem into two subproblems by setting (x + -0.8979591835) equal to 0.69267603 and -0.69267603.Subproblem 1
x + -0.8979591835 = 0.69267603 Simplifying x + -0.8979591835 = 0.69267603 Reorder the terms: -0.8979591835 + x = 0.69267603 Solving -0.8979591835 + x = 0.69267603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8979591835' to each side of the equation. -0.8979591835 + 0.8979591835 + x = 0.69267603 + 0.8979591835 Combine like terms: -0.8979591835 + 0.8979591835 = 0.0000000000 0.0000000000 + x = 0.69267603 + 0.8979591835 x = 0.69267603 + 0.8979591835 Combine like terms: 0.69267603 + 0.8979591835 = 1.5906352135 x = 1.5906352135 Simplifying x = 1.5906352135Subproblem 2
x + -0.8979591835 = -0.69267603 Simplifying x + -0.8979591835 = -0.69267603 Reorder the terms: -0.8979591835 + x = -0.69267603 Solving -0.8979591835 + x = -0.69267603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8979591835' to each side of the equation. -0.8979591835 + 0.8979591835 + x = -0.69267603 + 0.8979591835 Combine like terms: -0.8979591835 + 0.8979591835 = 0.0000000000 0.0000000000 + x = -0.69267603 + 0.8979591835 x = -0.69267603 + 0.8979591835 Combine like terms: -0.69267603 + 0.8979591835 = 0.2052831535 x = 0.2052831535 Simplifying x = 0.2052831535Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5906352135, 0.2052831535}
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