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Simplifying 9x(3 + 7x) = 2x + 19 (3 * 9x + 7x * 9x) = 2x + 19 (27x + 63x2) = 2x + 19 Reorder the terms: 27x + 63x2 = 19 + 2x Solving 27x + 63x2 = 19 + 2x Solving for variable 'x'. Reorder the terms: -19 + 27x + -2x + 63x2 = 19 + 2x + -19 + -2x Combine like terms: 27x + -2x = 25x -19 + 25x + 63x2 = 19 + 2x + -19 + -2x Reorder the terms: -19 + 25x + 63x2 = 19 + -19 + 2x + -2x Combine like terms: 19 + -19 = 0 -19 + 25x + 63x2 = 0 + 2x + -2x -19 + 25x + 63x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -19 + 25x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -0.3015873016 + 0.3968253968x + x2 = 0 Move the constant term to the right: Add '0.3015873016' to each side of the equation. -0.3015873016 + 0.3968253968x + 0.3015873016 + x2 = 0 + 0.3015873016 Reorder the terms: -0.3015873016 + 0.3015873016 + 0.3968253968x + x2 = 0 + 0.3015873016 Combine like terms: -0.3015873016 + 0.3015873016 = 0.0000000000 0.0000000000 + 0.3968253968x + x2 = 0 + 0.3015873016 0.3968253968x + x2 = 0 + 0.3015873016 Combine like terms: 0 + 0.3015873016 = 0.3015873016 0.3968253968x + x2 = 0.3015873016 The x term is 0.3968253968x. Take half its coefficient (0.1984126984). Square it (0.03936759889) and add it to both sides. Add '0.03936759889' to each side of the equation. 0.3968253968x + 0.03936759889 + x2 = 0.3015873016 + 0.03936759889 Reorder the terms: 0.03936759889 + 0.3968253968x + x2 = 0.3015873016 + 0.03936759889 Combine like terms: 0.3015873016 + 0.03936759889 = 0.34095490049 0.03936759889 + 0.3968253968x + x2 = 0.34095490049 Factor a perfect square on the left side: (x + 0.1984126984)(x + 0.1984126984) = 0.34095490049 Calculate the square root of the right side: 0.583913436 Break this problem into two subproblems by setting (x + 0.1984126984) equal to 0.583913436 and -0.583913436.Subproblem 1
x + 0.1984126984 = 0.583913436 Simplifying x + 0.1984126984 = 0.583913436 Reorder the terms: 0.1984126984 + x = 0.583913436 Solving 0.1984126984 + x = 0.583913436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1984126984' to each side of the equation. 0.1984126984 + -0.1984126984 + x = 0.583913436 + -0.1984126984 Combine like terms: 0.1984126984 + -0.1984126984 = 0.0000000000 0.0000000000 + x = 0.583913436 + -0.1984126984 x = 0.583913436 + -0.1984126984 Combine like terms: 0.583913436 + -0.1984126984 = 0.3855007376 x = 0.3855007376 Simplifying x = 0.3855007376Subproblem 2
x + 0.1984126984 = -0.583913436 Simplifying x + 0.1984126984 = -0.583913436 Reorder the terms: 0.1984126984 + x = -0.583913436 Solving 0.1984126984 + x = -0.583913436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1984126984' to each side of the equation. 0.1984126984 + -0.1984126984 + x = -0.583913436 + -0.1984126984 Combine like terms: 0.1984126984 + -0.1984126984 = 0.0000000000 0.0000000000 + x = -0.583913436 + -0.1984126984 x = -0.583913436 + -0.1984126984 Combine like terms: -0.583913436 + -0.1984126984 = -0.7823261344 x = -0.7823261344 Simplifying x = -0.7823261344Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3855007376, -0.7823261344}
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