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Simplifying (21x + -2)(38x + 5) = 360 Reorder the terms: (-2 + 21x)(38x + 5) = 360 Reorder the terms: (-2 + 21x)(5 + 38x) = 360 Multiply (-2 + 21x) * (5 + 38x) (-2(5 + 38x) + 21x * (5 + 38x)) = 360 ((5 * -2 + 38x * -2) + 21x * (5 + 38x)) = 360 ((-10 + -76x) + 21x * (5 + 38x)) = 360 (-10 + -76x + (5 * 21x + 38x * 21x)) = 360 (-10 + -76x + (105x + 798x2)) = 360 Combine like terms: -76x + 105x = 29x (-10 + 29x + 798x2) = 360 Solving -10 + 29x + 798x2 = 360 Solving for variable 'x'. Reorder the terms: -10 + -360 + 29x + 798x2 = 360 + -360 Combine like terms: -10 + -360 = -370 -370 + 29x + 798x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -370 + 29x + 798x2 = 0 Begin completing the square. Divide all terms by 798 the coefficient of the squared term: Divide each side by '798'. -0.4636591479 + 0.03634085213x + x2 = 0 Move the constant term to the right: Add '0.4636591479' to each side of the equation. -0.4636591479 + 0.03634085213x + 0.4636591479 + x2 = 0 + 0.4636591479 Reorder the terms: -0.4636591479 + 0.4636591479 + 0.03634085213x + x2 = 0 + 0.4636591479 Combine like terms: -0.4636591479 + 0.4636591479 = 0.0000000000 0.0000000000 + 0.03634085213x + x2 = 0 + 0.4636591479 0.03634085213x + x2 = 0 + 0.4636591479 Combine like terms: 0 + 0.4636591479 = 0.4636591479 0.03634085213x + x2 = 0.4636591479 The x term is 0.03634085213x. Take half its coefficient (0.01817042607). Square it (0.0003301643836) and add it to both sides. Add '0.0003301643836' to each side of the equation. 0.03634085213x + 0.0003301643836 + x2 = 0.4636591479 + 0.0003301643836 Reorder the terms: 0.0003301643836 + 0.03634085213x + x2 = 0.4636591479 + 0.0003301643836 Combine like terms: 0.4636591479 + 0.0003301643836 = 0.4639893122836 0.0003301643836 + 0.03634085213x + x2 = 0.4639893122836 Factor a perfect square on the left side: (x + 0.01817042607)(x + 0.01817042607) = 0.4639893122836 Calculate the square root of the right side: 0.68116761 Break this problem into two subproblems by setting (x + 0.01817042607) equal to 0.68116761 and -0.68116761.Subproblem 1
x + 0.01817042607 = 0.68116761 Simplifying x + 0.01817042607 = 0.68116761 Reorder the terms: 0.01817042607 + x = 0.68116761 Solving 0.01817042607 + x = 0.68116761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01817042607' to each side of the equation. 0.01817042607 + -0.01817042607 + x = 0.68116761 + -0.01817042607 Combine like terms: 0.01817042607 + -0.01817042607 = 0.00000000000 0.00000000000 + x = 0.68116761 + -0.01817042607 x = 0.68116761 + -0.01817042607 Combine like terms: 0.68116761 + -0.01817042607 = 0.66299718393 x = 0.66299718393 Simplifying x = 0.66299718393Subproblem 2
x + 0.01817042607 = -0.68116761 Simplifying x + 0.01817042607 = -0.68116761 Reorder the terms: 0.01817042607 + x = -0.68116761 Solving 0.01817042607 + x = -0.68116761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01817042607' to each side of the equation. 0.01817042607 + -0.01817042607 + x = -0.68116761 + -0.01817042607 Combine like terms: 0.01817042607 + -0.01817042607 = 0.00000000000 0.00000000000 + x = -0.68116761 + -0.01817042607 x = -0.68116761 + -0.01817042607 Combine like terms: -0.68116761 + -0.01817042607 = -0.69933803607 x = -0.69933803607 Simplifying x = -0.69933803607Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.66299718393, -0.69933803607}
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