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Simplifying (3x + -4)(64 + -1x) = 10 Reorder the terms: (-4 + 3x)(64 + -1x) = 10 Multiply (-4 + 3x) * (64 + -1x) (-4(64 + -1x) + 3x * (64 + -1x)) = 10 ((64 * -4 + -1x * -4) + 3x * (64 + -1x)) = 10 ((-256 + 4x) + 3x * (64 + -1x)) = 10 (-256 + 4x + (64 * 3x + -1x * 3x)) = 10 (-256 + 4x + (192x + -3x2)) = 10 Combine like terms: 4x + 192x = 196x (-256 + 196x + -3x2) = 10 Solving -256 + 196x + -3x2 = 10 Solving for variable 'x'. Reorder the terms: -256 + -10 + 196x + -3x2 = 10 + -10 Combine like terms: -256 + -10 = -266 -266 + 196x + -3x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -266 + 196x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 88.66666667 + -65.33333333x + x2 = 0 Move the constant term to the right: Add '-88.66666667' to each side of the equation. 88.66666667 + -65.33333333x + -88.66666667 + x2 = 0 + -88.66666667 Reorder the terms: 88.66666667 + -88.66666667 + -65.33333333x + x2 = 0 + -88.66666667 Combine like terms: 88.66666667 + -88.66666667 = 0.00000000 0.00000000 + -65.33333333x + x2 = 0 + -88.66666667 -65.33333333x + x2 = 0 + -88.66666667 Combine like terms: 0 + -88.66666667 = -88.66666667 -65.33333333x + x2 = -88.66666667 The x term is -65.33333333x. Take half its coefficient (-32.66666667). Square it (1067.111111) and add it to both sides. Add '1067.111111' to each side of the equation. -65.33333333x + 1067.111111 + x2 = -88.66666667 + 1067.111111 Reorder the terms: 1067.111111 + -65.33333333x + x2 = -88.66666667 + 1067.111111 Combine like terms: -88.66666667 + 1067.111111 = 978.44444433 1067.111111 + -65.33333333x + x2 = 978.44444433 Factor a perfect square on the left side: (x + -32.66666667)(x + -32.66666667) = 978.44444433 Calculate the square root of the right side: 31.280096616 Break this problem into two subproblems by setting (x + -32.66666667) equal to 31.280096616 and -31.280096616.Subproblem 1
x + -32.66666667 = 31.280096616 Simplifying x + -32.66666667 = 31.280096616 Reorder the terms: -32.66666667 + x = 31.280096616 Solving -32.66666667 + x = 31.280096616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.66666667' to each side of the equation. -32.66666667 + 32.66666667 + x = 31.280096616 + 32.66666667 Combine like terms: -32.66666667 + 32.66666667 = 0.00000000 0.00000000 + x = 31.280096616 + 32.66666667 x = 31.280096616 + 32.66666667 Combine like terms: 31.280096616 + 32.66666667 = 63.946763286 x = 63.946763286 Simplifying x = 63.946763286Subproblem 2
x + -32.66666667 = -31.280096616 Simplifying x + -32.66666667 = -31.280096616 Reorder the terms: -32.66666667 + x = -31.280096616 Solving -32.66666667 + x = -31.280096616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.66666667' to each side of the equation. -32.66666667 + 32.66666667 + x = -31.280096616 + 32.66666667 Combine like terms: -32.66666667 + 32.66666667 = 0.00000000 0.00000000 + x = -31.280096616 + 32.66666667 x = -31.280096616 + 32.66666667 Combine like terms: -31.280096616 + 32.66666667 = 1.386570054 x = 1.386570054 Simplifying x = 1.386570054Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.946763286, 1.386570054}
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