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Simplifying (x2 + -0.4x) + (-0.3x + 1) = 100 Reorder the terms: (-0.4x + x2) + (-0.3x + 1) = 100 Remove parenthesis around (-0.4x + x2) -0.4x + x2 + (-0.3x + 1) = 100 Reorder the terms: -0.4x + x2 + (1 + -0.3x) = 100 Remove parenthesis around (1 + -0.3x) -0.4x + x2 + 1 + -0.3x = 100 Reorder the terms: 1 + -0.4x + -0.3x + x2 = 100 Combine like terms: -0.4x + -0.3x = -0.7x 1 + -0.7x + x2 = 100 Solving 1 + -0.7x + x2 = 100 Solving for variable 'x'. Reorder the terms: 1 + -100 + -0.7x + x2 = 100 + -100 Combine like terms: 1 + -100 = -99 -99 + -0.7x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -99 + -0.7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -0.7x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -0.7x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -0.7x + x2 = 0 + 99 -0.7x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -0.7x + x2 = 99 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = 99 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 99 + 0.1225 Combine like terms: 99 + 0.1225 = 99.1225 0.1225 + -0.7x + x2 = 99.1225 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 99.1225 Calculate the square root of the right side: 9.956028325 Break this problem into two subproblems by setting (x + -0.35) equal to 9.956028325 and -9.956028325.Subproblem 1
x + -0.35 = 9.956028325 Simplifying x + -0.35 = 9.956028325 Reorder the terms: -0.35 + x = 9.956028325 Solving -0.35 + x = 9.956028325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 9.956028325 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 9.956028325 + 0.35 x = 9.956028325 + 0.35 Combine like terms: 9.956028325 + 0.35 = 10.306028325 x = 10.306028325 Simplifying x = 10.306028325Subproblem 2
x + -0.35 = -9.956028325 Simplifying x + -0.35 = -9.956028325 Reorder the terms: -0.35 + x = -9.956028325 Solving -0.35 + x = -9.956028325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = -9.956028325 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -9.956028325 + 0.35 x = -9.956028325 + 0.35 Combine like terms: -9.956028325 + 0.35 = -9.606028325 x = -9.606028325 Simplifying x = -9.606028325Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.306028325, -9.606028325}
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