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Simplifying 3(2x * 2x + -3) = 25x Reorder the terms for easier multiplication: 3(2 * 2x * x + -3) = 25x Multiply 2 * 2 3(4x * x + -3) = 25x Multiply x * x 3(4x2 + -3) = 25x Reorder the terms: 3(-3 + 4x2) = 25x (-3 * 3 + 4x2 * 3) = 25x (-9 + 12x2) = 25x Solving -9 + 12x2 = 25x Solving for variable 'x'. Reorder the terms: -9 + -25x + 12x2 = 25x + -25x Combine like terms: 25x + -25x = 0 -9 + -25x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.75 + -2.083333333x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2.083333333x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2.083333333x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2.083333333x + x2 = 0 + 0.75 -2.083333333x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2.083333333x + x2 = 0.75 The x term is -2.083333333x. Take half its coefficient (-1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. -2.083333333x + 1.085069445 + x2 = 0.75 + 1.085069445 Reorder the terms: 1.085069445 + -2.083333333x + x2 = 0.75 + 1.085069445 Combine like terms: 0.75 + 1.085069445 = 1.835069445 1.085069445 + -2.083333333x + x2 = 1.835069445 Factor a perfect square on the left side: (x + -1.041666667)(x + -1.041666667) = 1.835069445 Calculate the square root of the right side: 1.354647351 Break this problem into two subproblems by setting (x + -1.041666667) equal to 1.354647351 and -1.354647351.Subproblem 1
x + -1.041666667 = 1.354647351 Simplifying x + -1.041666667 = 1.354647351 Reorder the terms: -1.041666667 + x = 1.354647351 Solving -1.041666667 + x = 1.354647351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = 1.354647351 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = 1.354647351 + 1.041666667 x = 1.354647351 + 1.041666667 Combine like terms: 1.354647351 + 1.041666667 = 2.396314018 x = 2.396314018 Simplifying x = 2.396314018Subproblem 2
x + -1.041666667 = -1.354647351 Simplifying x + -1.041666667 = -1.354647351 Reorder the terms: -1.041666667 + x = -1.354647351 Solving -1.041666667 + x = -1.354647351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = -1.354647351 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = -1.354647351 + 1.041666667 x = -1.354647351 + 1.041666667 Combine like terms: -1.354647351 + 1.041666667 = -0.312980684 x = -0.312980684 Simplifying x = -0.312980684Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.396314018, -0.312980684}
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