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Simplifying 5x0 + 4x + -9.3x2 = 1x0 Solving 5 + 4x + -9.3x2 = 1 Solving for variable 'x'. Reorder the terms: 5 + -1 + 4x + -9.3x2 = 1 + -1 Combine like terms: 5 + -1 = 4 4 + 4x + -9.3x2 = 1 + -1 Combine like terms: 1 + -1 = 0 4 + 4x + -9.3x2 = 0 Begin completing the square. Divide all terms by -9.3 the coefficient of the squared term: Divide each side by '-9.3'. -0.4301075269 + -0.4301075269x + x2 = 0 Move the constant term to the right: Add '0.4301075269' to each side of the equation. -0.4301075269 + -0.4301075269x + 0.4301075269 + x2 = 0 + 0.4301075269 Reorder the terms: -0.4301075269 + 0.4301075269 + -0.4301075269x + x2 = 0 + 0.4301075269 Combine like terms: -0.4301075269 + 0.4301075269 = 0.0000000000 0.0000000000 + -0.4301075269x + x2 = 0 + 0.4301075269 -0.4301075269x + x2 = 0 + 0.4301075269 Combine like terms: 0 + 0.4301075269 = 0.4301075269 -0.4301075269x + x2 = 0.4301075269 The x term is -0.4301075269x. Take half its coefficient (-0.2150537635). Square it (0.04624812120) and add it to both sides. Add '0.04624812120' to each side of the equation. -0.4301075269x + 0.04624812120 + x2 = 0.4301075269 + 0.04624812120 Reorder the terms: 0.04624812120 + -0.4301075269x + x2 = 0.4301075269 + 0.04624812120 Combine like terms: 0.4301075269 + 0.04624812120 = 0.4763556481 0.04624812120 + -0.4301075269x + x2 = 0.4763556481 Factor a perfect square on the left side: (x + -0.2150537635)(x + -0.2150537635) = 0.4763556481 Calculate the square root of the right side: 0.690185227 Break this problem into two subproblems by setting (x + -0.2150537635) equal to 0.690185227 and -0.690185227.Subproblem 1
x + -0.2150537635 = 0.690185227 Simplifying x + -0.2150537635 = 0.690185227 Reorder the terms: -0.2150537635 + x = 0.690185227 Solving -0.2150537635 + x = 0.690185227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2150537635' to each side of the equation. -0.2150537635 + 0.2150537635 + x = 0.690185227 + 0.2150537635 Combine like terms: -0.2150537635 + 0.2150537635 = 0.0000000000 0.0000000000 + x = 0.690185227 + 0.2150537635 x = 0.690185227 + 0.2150537635 Combine like terms: 0.690185227 + 0.2150537635 = 0.9052389905 x = 0.9052389905 Simplifying x = 0.9052389905Subproblem 2
x + -0.2150537635 = -0.690185227 Simplifying x + -0.2150537635 = -0.690185227 Reorder the terms: -0.2150537635 + x = -0.690185227 Solving -0.2150537635 + x = -0.690185227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2150537635' to each side of the equation. -0.2150537635 + 0.2150537635 + x = -0.690185227 + 0.2150537635 Combine like terms: -0.2150537635 + 0.2150537635 = 0.0000000000 0.0000000000 + x = -0.690185227 + 0.2150537635 x = -0.690185227 + 0.2150537635 Combine like terms: -0.690185227 + 0.2150537635 = -0.4751314635 x = -0.4751314635 Simplifying x = -0.4751314635Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9052389905, -0.4751314635}
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