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Simplifying 9x2 + 30 = 10(3x + 5) + -25 Reorder the terms: 30 + 9x2 = 10(3x + 5) + -25 Reorder the terms: 30 + 9x2 = 10(5 + 3x) + -25 30 + 9x2 = (5 * 10 + 3x * 10) + -25 30 + 9x2 = (50 + 30x) + -25 Reorder the terms: 30 + 9x2 = 50 + -25 + 30x Combine like terms: 50 + -25 = 25 30 + 9x2 = 25 + 30x Solving 30 + 9x2 = 25 + 30x Solving for variable 'x'. Reorder the terms: 30 + -25 + -30x + 9x2 = 25 + 30x + -25 + -30x Combine like terms: 30 + -25 = 5 5 + -30x + 9x2 = 25 + 30x + -25 + -30x Reorder the terms: 5 + -30x + 9x2 = 25 + -25 + 30x + -30x Combine like terms: 25 + -25 = 0 5 + -30x + 9x2 = 0 + 30x + -30x 5 + -30x + 9x2 = 30x + -30x Combine like terms: 30x + -30x = 0 5 + -30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -3.333333333x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -3.333333333x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -3.333333333x + x2 = 0 + -0.5555555556 -3.333333333x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -3.333333333x + x2 = -0.5555555556 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -0.5555555556 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -0.5555555556 + 2.777777779 Combine like terms: -0.5555555556 + 2.777777779 = 2.2222222234 2.777777779 + -3.333333333x + x2 = 2.2222222234 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 2.2222222234 Calculate the square root of the right side: 1.490711985 Break this problem into two subproblems by setting (x + -1.666666667) equal to 1.490711985 and -1.490711985.Subproblem 1
x + -1.666666667 = 1.490711985 Simplifying x + -1.666666667 = 1.490711985 Reorder the terms: -1.666666667 + x = 1.490711985 Solving -1.666666667 + x = 1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 1.490711985 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 1.490711985 + 1.666666667 x = 1.490711985 + 1.666666667 Combine like terms: 1.490711985 + 1.666666667 = 3.157378652 x = 3.157378652 Simplifying x = 3.157378652Subproblem 2
x + -1.666666667 = -1.490711985 Simplifying x + -1.666666667 = -1.490711985 Reorder the terms: -1.666666667 + x = -1.490711985 Solving -1.666666667 + x = -1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -1.490711985 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -1.490711985 + 1.666666667 x = -1.490711985 + 1.666666667 Combine like terms: -1.490711985 + 1.666666667 = 0.175954682 x = 0.175954682 Simplifying x = 0.175954682Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.157378652, 0.175954682}
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