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Simplifying 3x2 + 8x + 4 = 19 Reorder the terms: 4 + 8x + 3x2 = 19 Solving 4 + 8x + 3x2 = 19 Solving for variable 'x'. Reorder the terms: 4 + -19 + 8x + 3x2 = 19 + -19 Combine like terms: 4 + -19 = -15 -15 + 8x + 3x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -15 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.666666667x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2.666666667x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.666666667x + x2 = 0 + 5 2.666666667x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.666666667x + x2 = 5 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 5 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 5 + 1.777777780 Combine like terms: 5 + 1.777777780 = 6.77777778 1.777777780 + 2.666666667x + x2 = 6.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 6.77777778 Calculate the square root of the right side: 2.603416559 Break this problem into two subproblems by setting (x + 1.333333334) equal to 2.603416559 and -2.603416559.Subproblem 1
x + 1.333333334 = 2.603416559 Simplifying x + 1.333333334 = 2.603416559 Reorder the terms: 1.333333334 + x = 2.603416559 Solving 1.333333334 + x = 2.603416559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 2.603416559 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 2.603416559 + -1.333333334 x = 2.603416559 + -1.333333334 Combine like terms: 2.603416559 + -1.333333334 = 1.270083225 x = 1.270083225 Simplifying x = 1.270083225Subproblem 2
x + 1.333333334 = -2.603416559 Simplifying x + 1.333333334 = -2.603416559 Reorder the terms: 1.333333334 + x = -2.603416559 Solving 1.333333334 + x = -2.603416559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -2.603416559 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -2.603416559 + -1.333333334 x = -2.603416559 + -1.333333334 Combine like terms: -2.603416559 + -1.333333334 = -3.936749893 x = -3.936749893 Simplifying x = -3.936749893Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.270083225, -3.936749893}
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