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Simplifying 4x + 35 = 3x(0.5x + 145.7) Reorder the terms: 35 + 4x = 3x(0.5x + 145.7) Reorder the terms: 35 + 4x = 3x(145.7 + 0.5x) 35 + 4x = (145.7 * 3x + 0.5x * 3x) 35 + 4x = (437.1x + 1.5x2) Solving 35 + 4x = 437.1x + 1.5x2 Solving for variable 'x'. Combine like terms: 4x + -437.1x = -433.1x 35 + -433.1x + -1.5x2 = 437.1x + 1.5x2 + -437.1x + -1.5x2 Reorder the terms: 35 + -433.1x + -1.5x2 = 437.1x + -437.1x + 1.5x2 + -1.5x2 Combine like terms: 437.1x + -437.1x = 0.0 35 + -433.1x + -1.5x2 = 0.0 + 1.5x2 + -1.5x2 35 + -433.1x + -1.5x2 = 1.5x2 + -1.5x2 Combine like terms: 1.5x2 + -1.5x2 = 0.0 35 + -433.1x + -1.5x2 = 0.0 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -23.33333333 + 288.7333333x + x2 = 0 Move the constant term to the right: Add '23.33333333' to each side of the equation. -23.33333333 + 288.7333333x + 23.33333333 + x2 = 0 + 23.33333333 Reorder the terms: -23.33333333 + 23.33333333 + 288.7333333x + x2 = 0 + 23.33333333 Combine like terms: -23.33333333 + 23.33333333 = 0.00000000 0.00000000 + 288.7333333x + x2 = 0 + 23.33333333 288.7333333x + x2 = 0 + 23.33333333 Combine like terms: 0 + 23.33333333 = 23.33333333 288.7333333x + x2 = 23.33333333 The x term is 288.7333333x. Take half its coefficient (144.3666667). Square it (20841.73445) and add it to both sides. Add '20841.73445' to each side of the equation. 288.7333333x + 20841.73445 + x2 = 23.33333333 + 20841.73445 Reorder the terms: 20841.73445 + 288.7333333x + x2 = 23.33333333 + 20841.73445 Combine like terms: 23.33333333 + 20841.73445 = 20865.06778333 20841.73445 + 288.7333333x + x2 = 20865.06778333 Factor a perfect square on the left side: (x + 144.3666667)(x + 144.3666667) = 20865.06778333 Calculate the square root of the right side: 144.447456825 Break this problem into two subproblems by setting (x + 144.3666667) equal to 144.447456825 and -144.447456825.Subproblem 1
x + 144.3666667 = 144.447456825 Simplifying x + 144.3666667 = 144.447456825 Reorder the terms: 144.3666667 + x = 144.447456825 Solving 144.3666667 + x = 144.447456825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-144.3666667' to each side of the equation. 144.3666667 + -144.3666667 + x = 144.447456825 + -144.3666667 Combine like terms: 144.3666667 + -144.3666667 = 0.0000000 0.0000000 + x = 144.447456825 + -144.3666667 x = 144.447456825 + -144.3666667 Combine like terms: 144.447456825 + -144.3666667 = 0.080790125 x = 0.080790125 Simplifying x = 0.080790125Subproblem 2
x + 144.3666667 = -144.447456825 Simplifying x + 144.3666667 = -144.447456825 Reorder the terms: 144.3666667 + x = -144.447456825 Solving 144.3666667 + x = -144.447456825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-144.3666667' to each side of the equation. 144.3666667 + -144.3666667 + x = -144.447456825 + -144.3666667 Combine like terms: 144.3666667 + -144.3666667 = 0.0000000 0.0000000 + x = -144.447456825 + -144.3666667 x = -144.447456825 + -144.3666667 Combine like terms: -144.447456825 + -144.3666667 = -288.814123525 x = -288.814123525 Simplifying x = -288.814123525Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.080790125, -288.814123525}
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