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Simplifying 36x2 + -84x + -49 = 12 Reorder the terms: -49 + -84x + 36x2 = 12 Solving -49 + -84x + 36x2 = 12 Solving for variable 'x'. Reorder the terms: -49 + -12 + -84x + 36x2 = 12 + -12 Combine like terms: -49 + -12 = -61 -61 + -84x + 36x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -61 + -84x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1.694444444 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '1.694444444' to each side of the equation. -1.694444444 + -2.333333333x + 1.694444444 + x2 = 0 + 1.694444444 Reorder the terms: -1.694444444 + 1.694444444 + -2.333333333x + x2 = 0 + 1.694444444 Combine like terms: -1.694444444 + 1.694444444 = 0.000000000 0.000000000 + -2.333333333x + x2 = 0 + 1.694444444 -2.333333333x + x2 = 0 + 1.694444444 Combine like terms: 0 + 1.694444444 = 1.694444444 -2.333333333x + x2 = 1.694444444 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 1.694444444 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 1.694444444 + 1.361111112 Combine like terms: 1.694444444 + 1.361111112 = 3.055555556 1.361111112 + -2.333333333x + x2 = 3.055555556 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 3.055555556 Calculate the square root of the right side: 1.748014747 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.748014747 and -1.748014747.Subproblem 1
x + -1.166666667 = 1.748014747 Simplifying x + -1.166666667 = 1.748014747 Reorder the terms: -1.166666667 + x = 1.748014747 Solving -1.166666667 + x = 1.748014747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.748014747 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.748014747 + 1.166666667 x = 1.748014747 + 1.166666667 Combine like terms: 1.748014747 + 1.166666667 = 2.914681414 x = 2.914681414 Simplifying x = 2.914681414Subproblem 2
x + -1.166666667 = -1.748014747 Simplifying x + -1.166666667 = -1.748014747 Reorder the terms: -1.166666667 + x = -1.748014747 Solving -1.166666667 + x = -1.748014747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.748014747 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.748014747 + 1.166666667 x = -1.748014747 + 1.166666667 Combine like terms: -1.748014747 + 1.166666667 = -0.58134808 x = -0.58134808 Simplifying x = -0.58134808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.914681414, -0.58134808}
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