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Simplifying 2x + 7 + 3x(x + -3) = 43 Reorder the terms: 2x + 7 + 3x(-3 + x) = 43 2x + 7 + (-3 * 3x + x * 3x) = 43 2x + 7 + (-9x + 3x2) = 43 Reorder the terms: 7 + 2x + -9x + 3x2 = 43 Combine like terms: 2x + -9x = -7x 7 + -7x + 3x2 = 43 Solving 7 + -7x + 3x2 = 43 Solving for variable 'x'. Reorder the terms: 7 + -43 + -7x + 3x2 = 43 + -43 Combine like terms: 7 + -43 = -36 -36 + -7x + 3x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -36 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -2.333333333x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -2.333333333x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -2.333333333x + x2 = 0 + 12 -2.333333333x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -2.333333333x + x2 = 12 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 = 12 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 12 + 1.361111112 Combine like terms: 12 + 1.361111112 = 13.361111112 1.361111112 + -2.333333333x + x2 = 13.361111112 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 13.361111112 Calculate the square root of the right side: 3.655285367 Break this problem into two subproblems by setting (x + -1.166666667) equal to 3.655285367 and -3.655285367.Subproblem 1
x + -1.166666667 = 3.655285367 Simplifying x + -1.166666667 = 3.655285367 Reorder the terms: -1.166666667 + x = 3.655285367 Solving -1.166666667 + x = 3.655285367 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 = 3.655285367 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 3.655285367 + 1.166666667 x = 3.655285367 + 1.166666667 Combine like terms: 3.655285367 + 1.166666667 = 4.821952034 x = 4.821952034 Simplifying x = 4.821952034Subproblem 2
x + -1.166666667 = -3.655285367 Simplifying x + -1.166666667 = -3.655285367 Reorder the terms: -1.166666667 + x = -3.655285367 Solving -1.166666667 + x = -3.655285367 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 = -3.655285367 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -3.655285367 + 1.166666667 x = -3.655285367 + 1.166666667 Combine like terms: -3.655285367 + 1.166666667 = -2.4886187 x = -2.4886187 Simplifying x = -2.4886187Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.821952034, -2.4886187}
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