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Simplifying 0.5(x + 2)(5x + 35) = 90x2 Reorder the terms: 0.5(2 + x)(5x + 35) = 90x2 Reorder the terms: 0.5(2 + x)(35 + 5x) = 90x2 Multiply (2 + x) * (35 + 5x) 0.5(2(35 + 5x) + x(35 + 5x)) = 90x2 0.5((35 * 2 + 5x * 2) + x(35 + 5x)) = 90x2 0.5((70 + 10x) + x(35 + 5x)) = 90x2 0.5(70 + 10x + (35 * x + 5x * x)) = 90x2 0.5(70 + 10x + (35x + 5x2)) = 90x2 Combine like terms: 10x + 35x = 45x 0.5(70 + 45x + 5x2) = 90x2 (70 * 0.5 + 45x * 0.5 + 5x2 * 0.5) = 90x2 (35 + 22.5x + 2.5x2) = 90x2 Solving 35 + 22.5x + 2.5x2 = 90x2 Solving for variable 'x'. Combine like terms: 2.5x2 + -90x2 = -87.5x2 35 + 22.5x + -87.5x2 = 90x2 + -90x2 Combine like terms: 90x2 + -90x2 = 0 35 + 22.5x + -87.5x2 = 0 Begin completing the square. Divide all terms by -87.5 the coefficient of the squared term: Divide each side by '-87.5'. -0.4 + -0.2571428571x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.2571428571x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.2571428571x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.2571428571x + x2 = 0 + 0.4 -0.2571428571x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.2571428571x + x2 = 0.4 The x term is -0.2571428571x. Take half its coefficient (-0.1285714286). Square it (0.01653061225) and add it to both sides. Add '0.01653061225' to each side of the equation. -0.2571428571x + 0.01653061225 + x2 = 0.4 + 0.01653061225 Reorder the terms: 0.01653061225 + -0.2571428571x + x2 = 0.4 + 0.01653061225 Combine like terms: 0.4 + 0.01653061225 = 0.41653061225 0.01653061225 + -0.2571428571x + x2 = 0.41653061225 Factor a perfect square on the left side: (x + -0.1285714286)(x + -0.1285714286) = 0.41653061225 Calculate the square root of the right side: 0.645391828 Break this problem into two subproblems by setting (x + -0.1285714286) equal to 0.645391828 and -0.645391828.Subproblem 1
x + -0.1285714286 = 0.645391828 Simplifying x + -0.1285714286 = 0.645391828 Reorder the terms: -0.1285714286 + x = 0.645391828 Solving -0.1285714286 + x = 0.645391828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1285714286' to each side of the equation. -0.1285714286 + 0.1285714286 + x = 0.645391828 + 0.1285714286 Combine like terms: -0.1285714286 + 0.1285714286 = 0.0000000000 0.0000000000 + x = 0.645391828 + 0.1285714286 x = 0.645391828 + 0.1285714286 Combine like terms: 0.645391828 + 0.1285714286 = 0.7739632566 x = 0.7739632566 Simplifying x = 0.7739632566Subproblem 2
x + -0.1285714286 = -0.645391828 Simplifying x + -0.1285714286 = -0.645391828 Reorder the terms: -0.1285714286 + x = -0.645391828 Solving -0.1285714286 + x = -0.645391828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1285714286' to each side of the equation. -0.1285714286 + 0.1285714286 + x = -0.645391828 + 0.1285714286 Combine like terms: -0.1285714286 + 0.1285714286 = 0.0000000000 0.0000000000 + x = -0.645391828 + 0.1285714286 x = -0.645391828 + 0.1285714286 Combine like terms: -0.645391828 + 0.1285714286 = -0.5168203994 x = -0.5168203994 Simplifying x = -0.5168203994Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7739632566, -0.5168203994}
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