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Simplifying -16x2 + 67x + 10 = 36 Reorder the terms: 10 + 67x + -16x2 = 36 Solving 10 + 67x + -16x2 = 36 Solving for variable 'x'. Reorder the terms: 10 + -36 + 67x + -16x2 = 36 + -36 Combine like terms: 10 + -36 = -26 -26 + 67x + -16x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -26 + 67x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.625 + -4.1875x + x2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -4.1875x + -1.625 + x2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + -4.1875x + x2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -4.1875x + x2 = 0 + -1.625 -4.1875x + x2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 -4.1875x + x2 = -1.625 The x term is -4.1875x. Take half its coefficient (-2.09375). Square it (4.383789063) and add it to both sides. Add '4.383789063' to each side of the equation. -4.1875x + 4.383789063 + x2 = -1.625 + 4.383789063 Reorder the terms: 4.383789063 + -4.1875x + x2 = -1.625 + 4.383789063 Combine like terms: -1.625 + 4.383789063 = 2.758789063 4.383789063 + -4.1875x + x2 = 2.758789063 Factor a perfect square on the left side: (x + -2.09375)(x + -2.09375) = 2.758789063 Calculate the square root of the right side: 1.660960283 Break this problem into two subproblems by setting (x + -2.09375) equal to 1.660960283 and -1.660960283.Subproblem 1
x + -2.09375 = 1.660960283 Simplifying x + -2.09375 = 1.660960283 Reorder the terms: -2.09375 + x = 1.660960283 Solving -2.09375 + x = 1.660960283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.09375' to each side of the equation. -2.09375 + 2.09375 + x = 1.660960283 + 2.09375 Combine like terms: -2.09375 + 2.09375 = 0.00000 0.00000 + x = 1.660960283 + 2.09375 x = 1.660960283 + 2.09375 Combine like terms: 1.660960283 + 2.09375 = 3.754710283 x = 3.754710283 Simplifying x = 3.754710283Subproblem 2
x + -2.09375 = -1.660960283 Simplifying x + -2.09375 = -1.660960283 Reorder the terms: -2.09375 + x = -1.660960283 Solving -2.09375 + x = -1.660960283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.09375' to each side of the equation. -2.09375 + 2.09375 + x = -1.660960283 + 2.09375 Combine like terms: -2.09375 + 2.09375 = 0.00000 0.00000 + x = -1.660960283 + 2.09375 x = -1.660960283 + 2.09375 Combine like terms: -1.660960283 + 2.09375 = 0.432789717 x = 0.432789717 Simplifying x = 0.432789717Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.754710283, 0.432789717}
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