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Simplifying -16x2 + 75x + 12 = 0 Reorder the terms: 12 + 75x + -16x2 = 0 Solving 12 + 75x + -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 + -4.6875x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -4.6875x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -4.6875x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -4.6875x + x2 = 0 + 0.75 -4.6875x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -4.6875x + x2 = 0.75 The x term is -4.6875x. Take half its coefficient (-2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. -4.6875x + 5.493164063 + x2 = 0.75 + 5.493164063 Reorder the terms: 5.493164063 + -4.6875x + x2 = 0.75 + 5.493164063 Combine like terms: 0.75 + 5.493164063 = 6.243164063 5.493164063 + -4.6875x + x2 = 6.243164063 Factor a perfect square on the left side: (x + -2.34375)(x + -2.34375) = 6.243164063 Calculate the square root of the right side: 2.498632439 Break this problem into two subproblems by setting (x + -2.34375) equal to 2.498632439 and -2.498632439.Subproblem 1
x + -2.34375 = 2.498632439 Simplifying x + -2.34375 = 2.498632439 Reorder the terms: -2.34375 + x = 2.498632439 Solving -2.34375 + x = 2.498632439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + x = 2.498632439 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + x = 2.498632439 + 2.34375 x = 2.498632439 + 2.34375 Combine like terms: 2.498632439 + 2.34375 = 4.842382439 x = 4.842382439 Simplifying x = 4.842382439Subproblem 2
x + -2.34375 = -2.498632439 Simplifying x + -2.34375 = -2.498632439 Reorder the terms: -2.34375 + x = -2.498632439 Solving -2.34375 + x = -2.498632439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + x = -2.498632439 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + x = -2.498632439 + 2.34375 x = -2.498632439 + 2.34375 Combine like terms: -2.498632439 + 2.34375 = -0.154882439 x = -0.154882439 Simplifying x = -0.154882439Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.842382439, -0.154882439}
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