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Simplifying 3x2 = 13x + 90 Reorder the terms: 3x2 = 90 + 13x Solving 3x2 = 90 + 13x Solving for variable 'x'. Reorder the terms: -90 + -13x + 3x2 = 90 + 13x + -90 + -13x Reorder the terms: -90 + -13x + 3x2 = 90 + -90 + 13x + -13x Combine like terms: 90 + -90 = 0 -90 + -13x + 3x2 = 0 + 13x + -13x -90 + -13x + 3x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -90 + -13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -4.333333333x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -4.333333333x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -4.333333333x + x2 = 0 + 30 -4.333333333x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -4.333333333x + x2 = 30 The x term is -4.333333333x. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333x + 4.694444446 + x2 = 30 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = 30 + 4.694444446 Combine like terms: 30 + 4.694444446 = 34.694444446 4.694444446 + -4.333333333x + x2 = 34.694444446 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 34.694444446 Calculate the square root of the right side: 5.890199016 Break this problem into two subproblems by setting (x + -2.166666667) equal to 5.890199016 and -5.890199016.Subproblem 1
x + -2.166666667 = 5.890199016 Simplifying x + -2.166666667 = 5.890199016 Reorder the terms: -2.166666667 + x = 5.890199016 Solving -2.166666667 + x = 5.890199016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 5.890199016 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 5.890199016 + 2.166666667 x = 5.890199016 + 2.166666667 Combine like terms: 5.890199016 + 2.166666667 = 8.056865683 x = 8.056865683 Simplifying x = 8.056865683Subproblem 2
x + -2.166666667 = -5.890199016 Simplifying x + -2.166666667 = -5.890199016 Reorder the terms: -2.166666667 + x = -5.890199016 Solving -2.166666667 + x = -5.890199016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -5.890199016 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -5.890199016 + 2.166666667 x = -5.890199016 + 2.166666667 Combine like terms: -5.890199016 + 2.166666667 = -3.723532349 x = -3.723532349 Simplifying x = -3.723532349Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.056865683, -3.723532349}
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