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Simplifying -16x2 + 15x + 12 = 0 Reorder the terms: 12 + 15x + -16x2 = 0 Solving 12 + 15x + -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'. -0.75 + -0.9375x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.9375x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.9375x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.9375x + x2 = 0 + 0.75 -0.9375x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.9375x + x2 = 0.75 The x term is -0.9375x. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375x + 0.2197265625 + x2 = 0.75 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375x + x2 = 0.75 + 0.2197265625 Combine like terms: 0.75 + 0.2197265625 = 0.9697265625 0.2197265625 + -0.9375x + x2 = 0.9697265625 Factor a perfect square on the left side: (x + -0.46875)(x + -0.46875) = 0.9697265625 Calculate the square root of the right side: 0.984746954 Break this problem into two subproblems by setting (x + -0.46875) equal to 0.984746954 and -0.984746954.Subproblem 1
x + -0.46875 = 0.984746954 Simplifying x + -0.46875 = 0.984746954 Reorder the terms: -0.46875 + x = 0.984746954 Solving -0.46875 + x = 0.984746954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + x = 0.984746954 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = 0.984746954 + 0.46875 x = 0.984746954 + 0.46875 Combine like terms: 0.984746954 + 0.46875 = 1.453496954 x = 1.453496954 Simplifying x = 1.453496954Subproblem 2
x + -0.46875 = -0.984746954 Simplifying x + -0.46875 = -0.984746954 Reorder the terms: -0.46875 + x = -0.984746954 Solving -0.46875 + x = -0.984746954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + x = -0.984746954 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = -0.984746954 + 0.46875 x = -0.984746954 + 0.46875 Combine like terms: -0.984746954 + 0.46875 = -0.515996954 x = -0.515996954 Simplifying x = -0.515996954Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.453496954, -0.515996954}
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