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Simplifying (5x + -3)(5x + -3) = 51 Reorder the terms: (-3 + 5x)(5x + -3) = 51 Reorder the terms: (-3 + 5x)(-3 + 5x) = 51 Multiply (-3 + 5x) * (-3 + 5x) (-3(-3 + 5x) + 5x * (-3 + 5x)) = 51 ((-3 * -3 + 5x * -3) + 5x * (-3 + 5x)) = 51 ((9 + -15x) + 5x * (-3 + 5x)) = 51 (9 + -15x + (-3 * 5x + 5x * 5x)) = 51 (9 + -15x + (-15x + 25x2)) = 51 Combine like terms: -15x + -15x = -30x (9 + -30x + 25x2) = 51 Solving 9 + -30x + 25x2 = 51 Solving for variable 'x'. Reorder the terms: 9 + -51 + -30x + 25x2 = 51 + -51 Combine like terms: 9 + -51 = -42 -42 + -30x + 25x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -42 + -30x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.68 + -1.2x + x2 = 0 Move the constant term to the right: Add '1.68' to each side of the equation. -1.68 + -1.2x + 1.68 + x2 = 0 + 1.68 Reorder the terms: -1.68 + 1.68 + -1.2x + x2 = 0 + 1.68 Combine like terms: -1.68 + 1.68 = 0.00 0.00 + -1.2x + x2 = 0 + 1.68 -1.2x + x2 = 0 + 1.68 Combine like terms: 0 + 1.68 = 1.68 -1.2x + x2 = 1.68 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 1.68 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 1.68 + 0.36 Combine like terms: 1.68 + 0.36 = 2.04 0.36 + -1.2x + x2 = 2.04 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (x + -0.6) equal to 1.428285686 and -1.428285686.Subproblem 1
x + -0.6 = 1.428285686 Simplifying x + -0.6 = 1.428285686 Reorder the terms: -0.6 + x = 1.428285686 Solving -0.6 + x = 1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.428285686 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.428285686 + 0.6 x = 1.428285686 + 0.6 Combine like terms: 1.428285686 + 0.6 = 2.028285686 x = 2.028285686 Simplifying x = 2.028285686Subproblem 2
x + -0.6 = -1.428285686 Simplifying x + -0.6 = -1.428285686 Reorder the terms: -0.6 + x = -1.428285686 Solving -0.6 + x = -1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.428285686 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.428285686 + 0.6 x = -1.428285686 + 0.6 Combine like terms: -1.428285686 + 0.6 = -0.828285686 x = -0.828285686 Simplifying x = -0.828285686Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.028285686, -0.828285686}
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