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Simplifying -16x2 + 5.8x + 1.5 = 0 Reorder the terms: 1.5 + 5.8x + -16x2 = 0 Solving 1.5 + 5.8x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.09375 + -0.3625x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + -0.3625x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + -0.3625x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + -0.3625x + x2 = 0 + 0.09375 -0.3625x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 -0.3625x + x2 = 0.09375 The x term is -0.3625x. Take half its coefficient (-0.18125). Square it (0.0328515625) and add it to both sides. Add '0.0328515625' to each side of the equation. -0.3625x + 0.0328515625 + x2 = 0.09375 + 0.0328515625 Reorder the terms: 0.0328515625 + -0.3625x + x2 = 0.09375 + 0.0328515625 Combine like terms: 0.09375 + 0.0328515625 = 0.1266015625 0.0328515625 + -0.3625x + x2 = 0.1266015625 Factor a perfect square on the left side: (x + -0.18125)(x + -0.18125) = 0.1266015625 Calculate the square root of the right side: 0.355811133 Break this problem into two subproblems by setting (x + -0.18125) equal to 0.355811133 and -0.355811133.Subproblem 1
x + -0.18125 = 0.355811133 Simplifying x + -0.18125 = 0.355811133 Reorder the terms: -0.18125 + x = 0.355811133 Solving -0.18125 + x = 0.355811133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.18125' to each side of the equation. -0.18125 + 0.18125 + x = 0.355811133 + 0.18125 Combine like terms: -0.18125 + 0.18125 = 0.00000 0.00000 + x = 0.355811133 + 0.18125 x = 0.355811133 + 0.18125 Combine like terms: 0.355811133 + 0.18125 = 0.537061133 x = 0.537061133 Simplifying x = 0.537061133Subproblem 2
x + -0.18125 = -0.355811133 Simplifying x + -0.18125 = -0.355811133 Reorder the terms: -0.18125 + x = -0.355811133 Solving -0.18125 + x = -0.355811133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.18125' to each side of the equation. -0.18125 + 0.18125 + x = -0.355811133 + 0.18125 Combine like terms: -0.18125 + 0.18125 = 0.00000 0.00000 + x = -0.355811133 + 0.18125 x = -0.355811133 + 0.18125 Combine like terms: -0.355811133 + 0.18125 = -0.174561133 x = -0.174561133 Simplifying x = -0.174561133Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.537061133, -0.174561133}
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