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Simplifying 2x2 + 8x + 4x2 + -7x + -3 = 33 Reorder the terms: -3 + 8x + -7x + 2x2 + 4x2 = 33 Combine like terms: 8x + -7x = 1x -3 + 1x + 2x2 + 4x2 = 33 Combine like terms: 2x2 + 4x2 = 6x2 -3 + 1x + 6x2 = 33 Solving -3 + 1x + 6x2 = 33 Solving for variable 'x'. Reorder the terms: -3 + -33 + 1x + 6x2 = 33 + -33 Combine like terms: -3 + -33 = -36 -36 + 1x + 6x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -36 + 1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 0.1666666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 0.1666666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 0.1666666667x + x2 = 0 + 6 0.1666666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 0.1666666667x + x2 = 6 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 6 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 6 + 0.006944444447 Combine like terms: 6 + 0.006944444447 = 6.006944444447 0.006944444447 + 0.1666666667x + x2 = 6.006944444447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 6.006944444447 Calculate the square root of the right side: 2.450906862 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 2.450906862 and -2.450906862.Subproblem 1
x + 0.08333333335 = 2.450906862 Simplifying x + 0.08333333335 = 2.450906862 Reorder the terms: 0.08333333335 + x = 2.450906862 Solving 0.08333333335 + x = 2.450906862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 2.450906862 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 2.450906862 + -0.08333333335 x = 2.450906862 + -0.08333333335 Combine like terms: 2.450906862 + -0.08333333335 = 2.36757352865 x = 2.36757352865 Simplifying x = 2.36757352865Subproblem 2
x + 0.08333333335 = -2.450906862 Simplifying x + 0.08333333335 = -2.450906862 Reorder the terms: 0.08333333335 + x = -2.450906862 Solving 0.08333333335 + x = -2.450906862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -2.450906862 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -2.450906862 + -0.08333333335 x = -2.450906862 + -0.08333333335 Combine like terms: -2.450906862 + -0.08333333335 = -2.53424019535 x = -2.53424019535 Simplifying x = -2.53424019535Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.36757352865, -2.53424019535}
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