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Simplifying 11.7 = -0.032x2 + 0.95x + 6.3 Reorder the terms: 11.7 = 6.3 + 0.95x + -0.032x2 Solving 11.7 = 6.3 + 0.95x + -0.032x2 Solving for variable 'x'. Combine like terms: 11.7 + -6.3 = 5.4 5.4 + -0.95x + 0.032x2 = 6.3 + 0.95x + -0.032x2 + -6.3 + -0.95x + 0.032x2 Reorder the terms: 5.4 + -0.95x + 0.032x2 = 6.3 + -6.3 + 0.95x + -0.95x + -0.032x2 + 0.032x2 Combine like terms: 6.3 + -6.3 = 0.0 5.4 + -0.95x + 0.032x2 = 0.0 + 0.95x + -0.95x + -0.032x2 + 0.032x2 5.4 + -0.95x + 0.032x2 = 0.95x + -0.95x + -0.032x2 + 0.032x2 Combine like terms: 0.95x + -0.95x = 0.00 5.4 + -0.95x + 0.032x2 = 0.00 + -0.032x2 + 0.032x2 5.4 + -0.95x + 0.032x2 = -0.032x2 + 0.032x2 Combine like terms: -0.032x2 + 0.032x2 = 0.000 5.4 + -0.95x + 0.032x2 = 0.000 Begin completing the square. Divide all terms by 0.032 the coefficient of the squared term: Divide each side by '0.032'. 168.75 + -29.6875x + x2 = 0 Move the constant term to the right: Add '-168.75' to each side of the equation. 168.75 + -29.6875x + -168.75 + x2 = 0 + -168.75 Reorder the terms: 168.75 + -168.75 + -29.6875x + x2 = 0 + -168.75 Combine like terms: 168.75 + -168.75 = 0.00 0.00 + -29.6875x + x2 = 0 + -168.75 -29.6875x + x2 = 0 + -168.75 Combine like terms: 0 + -168.75 = -168.75 -29.6875x + x2 = -168.75 The x term is -29.6875x. Take half its coefficient (-14.84375). Square it (220.3369141) and add it to both sides. Add '220.3369141' to each side of the equation. -29.6875x + 220.3369141 + x2 = -168.75 + 220.3369141 Reorder the terms: 220.3369141 + -29.6875x + x2 = -168.75 + 220.3369141 Combine like terms: -168.75 + 220.3369141 = 51.5869141 220.3369141 + -29.6875x + x2 = 51.5869141 Factor a perfect square on the left side: (x + -14.84375)(x + -14.84375) = 51.5869141 Calculate the square root of the right side: 7.182403087 Break this problem into two subproblems by setting (x + -14.84375) equal to 7.182403087 and -7.182403087.Subproblem 1
x + -14.84375 = 7.182403087 Simplifying x + -14.84375 = 7.182403087 Reorder the terms: -14.84375 + x = 7.182403087 Solving -14.84375 + x = 7.182403087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.84375' to each side of the equation. -14.84375 + 14.84375 + x = 7.182403087 + 14.84375 Combine like terms: -14.84375 + 14.84375 = 0.00000 0.00000 + x = 7.182403087 + 14.84375 x = 7.182403087 + 14.84375 Combine like terms: 7.182403087 + 14.84375 = 22.026153087 x = 22.026153087 Simplifying x = 22.026153087Subproblem 2
x + -14.84375 = -7.182403087 Simplifying x + -14.84375 = -7.182403087 Reorder the terms: -14.84375 + x = -7.182403087 Solving -14.84375 + x = -7.182403087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.84375' to each side of the equation. -14.84375 + 14.84375 + x = -7.182403087 + 14.84375 Combine like terms: -14.84375 + 14.84375 = 0.00000 0.00000 + x = -7.182403087 + 14.84375 x = -7.182403087 + 14.84375 Combine like terms: -7.182403087 + 14.84375 = 7.661346913 x = 7.661346913 Simplifying x = 7.661346913Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.026153087, 7.661346913}
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