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Simplifying -24x2 + 55x = 7 Reorder the terms: 55x + -24x2 = 7 Solving 55x + -24x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 55x + -24x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 55x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. 0.2916666667 + -2.291666667x + x2 = 0 Move the constant term to the right: Add '-0.2916666667' to each side of the equation. 0.2916666667 + -2.291666667x + -0.2916666667 + x2 = 0 + -0.2916666667 Reorder the terms: 0.2916666667 + -0.2916666667 + -2.291666667x + x2 = 0 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + -2.291666667x + x2 = 0 + -0.2916666667 -2.291666667x + x2 = 0 + -0.2916666667 Combine like terms: 0 + -0.2916666667 = -0.2916666667 -2.291666667x + x2 = -0.2916666667 The x term is -2.291666667x. Take half its coefficient (-1.145833334). Square it (1.312934029) and add it to both sides. Add '1.312934029' to each side of the equation. -2.291666667x + 1.312934029 + x2 = -0.2916666667 + 1.312934029 Reorder the terms: 1.312934029 + -2.291666667x + x2 = -0.2916666667 + 1.312934029 Combine like terms: -0.2916666667 + 1.312934029 = 1.0212673623 1.312934029 + -2.291666667x + x2 = 1.0212673623 Factor a perfect square on the left side: (x + -1.145833334)(x + -1.145833334) = 1.0212673623 Calculate the square root of the right side: 1.010577737 Break this problem into two subproblems by setting (x + -1.145833334) equal to 1.010577737 and -1.010577737.Subproblem 1
x + -1.145833334 = 1.010577737 Simplifying x + -1.145833334 = 1.010577737 Reorder the terms: -1.145833334 + x = 1.010577737 Solving -1.145833334 + x = 1.010577737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.145833334' to each side of the equation. -1.145833334 + 1.145833334 + x = 1.010577737 + 1.145833334 Combine like terms: -1.145833334 + 1.145833334 = 0.000000000 0.000000000 + x = 1.010577737 + 1.145833334 x = 1.010577737 + 1.145833334 Combine like terms: 1.010577737 + 1.145833334 = 2.156411071 x = 2.156411071 Simplifying x = 2.156411071Subproblem 2
x + -1.145833334 = -1.010577737 Simplifying x + -1.145833334 = -1.010577737 Reorder the terms: -1.145833334 + x = -1.010577737 Solving -1.145833334 + x = -1.010577737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.145833334' to each side of the equation. -1.145833334 + 1.145833334 + x = -1.010577737 + 1.145833334 Combine like terms: -1.145833334 + 1.145833334 = 0.000000000 0.000000000 + x = -1.010577737 + 1.145833334 x = -1.010577737 + 1.145833334 Combine like terms: -1.010577737 + 1.145833334 = 0.135255597 x = 0.135255597 Simplifying x = 0.135255597Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.156411071, 0.135255597}
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